論文紹介: MDCC: Multi-Data Center Consistency (EuroSys '13)

Transcript

1. 論文紹介: MDCC: Multi-Data Center Consistency (EuroSys ’13) Youki Shiraishi June 5, 2023
2. 論文の概要 MDCC: Multi-Data Center Consistency Tim Kraska Gene Pang Michael J. Franklin Samuel Madden Alan Fekete† University of California, Berkeley MIT †University of Sydney {kraska, gpang, franklin}@cs.berkeley.edu madden@csail.mit.edu alan.fekete@sydney.edu.au Abstract Replicating data across multiple data centers allows using data closer to the client, reducing latency for applications, and increases the availability in the event of a data cen- ter failure. MDCC (Multi-Data Center Consistency) is an optimistic commit protocol for geo-replicated transactions, that does not require a master or static partitioning, and is strongly consistent at a cost similar to eventually consis- tent protocols. MDCC takes advantage of Generalized Paxos for transaction processing and exploits commutative updates with value constraints in a quorum-based system. Our exper- iments show that MDCC outperforms existing synchronous taken between data centers, and desirable to avoid waiting for the slowest data center to respond. For database-backed applications, it is a very valuable feature when the system supports transactions: multiple op- erations (such as individual reads and writes) grouped to- gether, with the system ensuring at least atomicity so that all changes made within the transaction are eventually persisted or none. The traditional mechanism for transactions that are distributed across databases is two-phase commit (2PC), but this has serious drawbacks in a geo-replicated system. 2PC depends on a reliable coordinator to determine the outcome of a transaction, so it will block for the duration of a coordi- • Read committed を保証する楽観的分散トランザクションコミットプロトコル MDCC [1] を 提案．行ごとに Generalized Paxos を実行し，トランザクションの可換性を活用しながら高 速クォーラムでのコミットを試みることで，通常 1 RTT のコミット遅延を実現． • 2PC や Megastore と比較してコミット遅延を約 50 % 削減，ログレプリケーションのボト ルネックを解消してスケーラビリティを向上． 1
3. Introduction
4. Megastore におけるトランザクション Figure 1: Scalable Replication are collaborative and have no single permanent owner. We create a second class of entity groups to hold the posts and metadata for each blog. A third class keys off the unique name claimed by each blog. The appli- cation relies on asynchronous messaging when a sin- gle user operation affects both blogs and profiles. For a lower-traffic operation like creating a new blog and claiming its unique name, two-phase commit is more convenient and performs adequately. Maps Geographic data has no natural granularity of any consistent or convenient size. A mapping application can create entity groups by dividing the globe into non- overlapping patches. For mutations that span patches, the application uses two-phase commit to make them atomic. Patches must be large enough that two-phase transactions are uncommon, but small enough that each patch requires only a small write throughput. Unlike the previous examples, the number of entity groups does not grow with increased usage, so enough patches must be created initially for sufficient aggre- gate throughput at later scale. Nearly all applications built on Megastore have found nat- ural ways to draw entity group boundaries. Figure 1: Scalable Replication Figure 2: Operations Across Entity Groups replicated via Paxos). Operations across entity groups could rely on expensive two-phase commits, but typically leverage Megastore’s efficient asynchronous messaging. A transac- tion in a sending entity group places one or more messages in a queue; transactions in receiving entity groups atomically consume those messages and apply ensuing mutations. Note that we use asynchronous messaging between logi- cally distant entity groups, not physically distant replicas. All network traffic between datacenters is from replicated M ur 2 st ar ac ti se w us gr m of fo • Single-decree Fast Paxos を用いて各シャードの WAL を同期レプリケーション． • (2PC +) ROMV + OCC を用いて (分散) トランザクションを実行． 2
5. Megastore とその系譜の問題点 • Megastore [2] は，コミット時にシャードごとに Paxos を実行してログエントリに対する合 意を形成し，トランザクションの全順序を決定する．すなわち，各シャードで一度に 1 つ のトランザクションしか実行できず，スケーラビリティのボトルネックとなる． • Spanner [3] は，動的リシャーディングとスナップショット分離のサポートにより性能を改 善，Paxos-CP [4] は，コンフリクトしないトランザクションを 1 つのログエントリでコミッ トすることにより性能を改善するが，前述のボトルネックは解消できていない． • その他にも 2PC やシングルマスターによるデメリットが多々ある． 3
6. MDCC (Multi-Data Center Consistency) • 通常 1 WAN RTT でトランザクションをコミット可能な楽観的コミットプロトコル． • さまざまな分離レベルをサポート可能．デフォルトは read committed w/o lost update． • 主な提案は以下の 3 つ． • 行ごとに Paxos を実行することでスケーラビリティのボトルネックを解消． • Fast Paxos を適用することで，衝突のない場合にマスターバイパス (単一のリーダーへ のアクセスを回避) と 1 WAN RTT のコミット遅延を実現． • Generalized Paxos によりトランザクションの可換性を活用して衝突を低減． • AWS の 5 つの DC を用いた TPC-W ベンチマークで，2PC や Megastore と比較して 50 % の コミット遅延となることを示した． 4
7. Architecture Overview
8. MDCC のアーキテクチャ • アプリケーションサーバーあるいはストレージサー バーは，レプリケーションにおける調停とトランザ クションマネージャーとしての役割を担う． • MDCC では行ごとにマスターが存在する．行の更新 における調停は，その行のマスターのストレージサ ーバー (黒矢印)，あるいはマスターシップを持たな いアプリケーションサーバー (赤矢印) が担う． • 以降は，各 DC が完全なレプリカを保持しているこ と，データが DC 内のサーバーでパーティション化 されていることを前提とする． Data center IV Data center III Data center I Data center II Application Servers Storage Servers Master Server Figure 1. MDCC architecture more horizontal partitions. Although not required, we as- sume for the remainder of the paper that every data center contains a full replica of the data, and the data within a sin- gle data center is partitioned across machines. The DB library provides a programming model for trans- actions and is mainly responsible for coordinating the repli- cation and consistency of the data using MDCC’s commit protocol. The DB library also acts as a transaction manager 5
9. The MDCC Protocol
10. MDCC プロトコルの構成 MDCC プロトコルは，次の 2 種類の Multi-Paxos イ ンスタンスを実行する． • 行ごとの Multi-Paxos インスタンス 行の変更 (更新や削除) をログとしてストレー ジノードに複製する． • テーブルごとの Multi-Paxos インスタンス テーブルに存在しない行の挿入をログとして ストレージノードに複製する． <latexit sha1_base64="nO2prTunTsglLGiKVpvuJMKbelc=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKr2PAi8cI5gHJEmZnZ5MxszvLTG8ghPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXkEph0HW/ncLa+sbmVnG7tLO7t39QPjxqGpVpxhtMSaXbATVcioQ3UKDk7VRzGgeSt4Lh3cxvjbg2QiWPOE65H9N+IiLBKFqp2R2FCk2vXHGr7hxklXg5qUCOeq/81Q0Vy2KeIJPUmI7npuhPqEbBJJ+WupnhKWVD2ucdSxMac+NP5tdOyZlVQhIpbStBMld/T0xobMw4DmxnTHFglr2Z+J/XyTC69SciSTPkCVssijJJUJHZ6yQUmjOUY0so08LeStiAasrQBlSyIXjLL6+S5kXVu65ePVxWaiSPowgncArn4MEN1OAe6tAABk/wDK/w5ijnxXl3PhatBSefOYY/cD5/AMR1jyo=</latexit> . . . <latexit 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sha1_base64="kgzki4oKtHt8M1hCiWltT9OsVCA=">AAAB9XicbVDJSgNBEO2JW4xb1KOXxkHwFGbE7Rjw4jGCWSAzhp5OTdKkZ7G7Rg1D/sOLB0W8+i/e/Bs7y0ETHxQ83quiql6QSqHRcb6twtLyyupacb20sbm1vVPe3WvoJFMc6jyRiWoFTIMUMdRRoIRWqoBFgYRmMLga+80HUFok8S0OU/Aj1otFKDhDI915CE8YhLlna7gfdcq2U3EmoIvEnRGbzFDrlL+8bsKzCGLkkmnddp0U/ZwpFFzCqORlGlLGB6wHbUNjFoH288nVI3pklC4NE2UqRjpRf0/kLNJ6GAWmM2LY1/PeWPzPa2cYXvq5iNMMIebTRWEmKSZ0HAHtCgUc5dAQxpUwt1LeZ4pxNEGVTAju/MuLpHFScc8rZzendpXO4iiSA3JIjolLLkiVXJMaqRNOFHkmr+TNerRerHfrY9pasGYz++QPrM8fwyiSlw==</latexit> #seq <latexit sha1_base64="LWRGAY1AzR9cg9mexPTnmyEKhW0=">AAAB83icbVDLSsNAFJ3UV62vqks3g0VwVRLxtSy4cVnB1kITymR60w6dTMLMjVhCf8ONC0Xc+jPu/BunbRbaemDgcM653DsnTKUw6LrfTmlldW19o7xZ2dre2d2r7h+0TZJpDi2eyER3QmZACgUtFCihk2pgcSjhIRzdTP2HR9BGJOoexykEMRsoEQnO0Eq+j/CEYZTbyKRXrbl1dwa6TLyC1EiBZq/65fcTnsWgkEtmTNdzUwxyplFwCZOKnxlIGR+xAXQtVSwGE+Szmyf0xCp9GiXaPoV0pv6eyFlszDgObTJmODSL3lT8z+tmGF0HuVBphqD4fFGUSYoJnRZA+0IDRzm2hHEt7K2UD5lmHG1NFVuCt/jlZdI+q3uX9Yu781qDFnWUyRE5JqfEI1ekQW5Jk7QIJyl5Jq/kzcmcF+fd+ZhHS04xc0j+wPn8AbWhkgg=</latexit> ver <latexit sha1_base64="kgzki4oKtHt8M1hCiWltT9OsVCA=">AAAB9XicbVDJSgNBEO2JW4xb1KOXxkHwFGbE7Rjw4jGCWSAzhp5OTdKkZ7G7Rg1D/sOLB0W8+i/e/Bs7y0ETHxQ83quiql6QSqHRcb6twtLyyupacb20sbm1vVPe3WvoJFMc6jyRiWoFTIMUMdRRoIRWqoBFgYRmMLga+80HUFok8S0OU/Aj1otFKDhDI915CE8YhLlna7gfdcq2U3EmoIvEnRGbzFDrlL+8bsKzCGLkkmnddp0U/ZwpFFzCqORlGlLGB6wHbUNjFoH288nVI3pklC4NE2UqRjpRf0/kLNJ6GAWmM2LY1/PeWPzPa2cYXvq5iNMMIebTRWEmKSZ0HAHtCgUc5dAQxpUwt1LeZ4pxNEGVTAju/MuLpHFScc8rZzendpXO4iiSA3JIjolLLkiVXJMaqRNOFHkmr+TNerRerHfrY9pasGYz++QPrM8fwyiSlw==</latexit> #seq <latexit sha1_base64="LWRGAY1AzR9cg9mexPTnmyEKhW0=">AAAB83icbVDLSsNAFJ3UV62vqks3g0VwVRLxtSy4cVnB1kITymR60w6dTMLMjVhCf8ONC0Xc+jPu/BunbRbaemDgcM653DsnTKUw6LrfTmlldW19o7xZ2dre2d2r7h+0TZJpDi2eyER3QmZACgUtFCihk2pgcSjhIRzdTP2HR9BGJOoexykEMRsoEQnO0Eq+j/CEYZTbyKRXrbl1dwa6TLyC1EiBZq/65fcTnsWgkEtmTNdzUwxyplFwCZOKnxlIGR+xAXQtVSwGE+Szmyf0xCp9GiXaPoV0pv6eyFlszDgObTJmODSL3lT8z+tmGF0HuVBphqD4fFGUSYoJnRZA+0IDRzm2hHEt7K2UD5lmHG1NFVuCt/jlZdI+q3uX9Yu781qDFnWUyRE5JqfEI1ekQW5Jk7QIJyl5Jq/kzcmcF+fd+ZhHS04xc0j+wPn8AbWhkgg=</latexit> ver <latexit sha1_base64="DUTHrYsSDUSGIHVIePsEn4U8J2s=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0nEr2PBi8eK1hbaUDbbTbt0swm7EyGE/gQvHhTx6i/y5r9x2+agrQ8GHu/NMDMvSKQw6LrfTmlldW19o7xZ2dre2d2r7h88mjjVjLdYLGPdCajhUijeQoGSdxLNaRRI3g7GN1O//cS1EbF6wCzhfkSHSoSCUbTSfdZ3+9WaW3dnIMvEK0gNCjT71a/eIGZpxBUySY3pem6Cfk41Cib5pNJLDU8oG9Mh71qqaMSNn89OnZATqwxIGGtbCslM/T2R08iYLApsZ0RxZBa9qfif100xvPZzoZIUuWLzRWEqCcZk+jcZCM0ZyswSyrSwtxI2opoytOlUbAje4svL5PGs7l3WL+7Oaw1SxFGGIziGU/DgChpwC01oAYMhPMMrvDnSeXHenY95a8kpZg7hD5zPHwS4jYg=</latexit> y0 <latexit sha1_base64="DJZMiTQxnl+dH+IcO58zRU/sfCQ=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0nEr2PBi8eK1hbaUDbbTbt0swm7EyGE/gQvHhTx6i/y5r9x2+agrQ8GHu/NMDMvSKQw6LrfTmlldW19o7xZ2dre2d2r7h88mjjVjLdYLGPdCajhUijeQoGSdxLNaRRI3g7GN1O//cS1EbF6wCzhfkSHSoSCUbTSfdb3+tWaW3dnIMvEK0gNCjT71a/eIGZpxBUySY3pem6Cfk41Cib5pNJLDU8oG9Mh71qqaMSNn89OnZATqwxIGGtbCslM/T2R08iYLApsZ0RxZBa9qfif100xvPZzoZIUuWLzRWEqCcZk+jcZCM0ZyswSyrSwtxI2opoytOlUbAje4svL5PGs7l3WL+7Oaw1SxFGGIziGU/DgChpwC01oAYMhPMMrvDnSeXHenY95a8kpZg7hD5zPHwY8jYk=</latexit> y1 <latexit sha1_base64="fpOUP9RYMQm+quQM2279uiBCeU4=">AAAB6HicbVDLSgNBEOyNrxhfUY9eBoPgKeyKr2PAi8cEzAOSJcxOepMxs7PLzKwQlnyBFw+KePWTvPk3TpI9aGJBQ1HVTXdXkAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4bua3n1BpHssHM0nQj+hQ8pAzaqzU8Prlilt15yCrxMtJBXLU++Wv3iBmaYTSMEG17npuYvyMKsOZwGmpl2pMKBvTIXYtlTRC7WfzQ6fkzCoDEsbKljRkrv6eyGik9SQKbGdEzUgvezPxP6+bmvDWz7hMUoOSLRaFqSAmJrOvyYArZEZMLKFMcXsrYSOqKDM2m5INwVt+eZW0LqredfWqcVmpkTyOIpzAKZyDBzdQg3uoQxMYIDzDK7w5j86L8+58LFoLTj5zDH/gfP4Ac6OMnQ==</latexit> 1 <latexit sha1_base64="pIVZpONp5sw1Q3+T+sIzrzjkUl4=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKr2PAi8eI5gHJEmYns8mQ2dllpleISz7BiwdFvPpF3vwbJ8keNLGgoajqprsrSKQw6LrfTmFldW19o7hZ2tre2d0r7x80TZxqxhsslrFuB9RwKRRvoEDJ24nmNAokbwWjm6nfeuTaiFg94DjhfkQHSoSCUbTS/VPP7ZUrbtWdgSwTLycVyFHvlb+6/ZilEVfIJDWm47kJ+hnVKJjkk1I3NTyhbEQHvGOpohE3fjY7dUJOrNInYaxtKSQz9fdERiNjxlFgOyOKQ7PoTcX/vE6K4bWfCZWkyBWbLwpTSTAm079JX2jOUI4toUwLeythQ6opQ5tOyYbgLb68TJpnVe+yenF3XqmRPI4iHMExnIIHV1CDW6hDAxgM4Ble4c2Rzovz7nzMWwtOPnMIf+B8/gAGPo2J</latexit> z0 <latexit sha1_base64="rLm8TD39zMcSFK0UVqXvleVg06A=">AAAB9XicbVDLSgMxFL1TX7W+qi7dBIvgqsyIr2XBjcsKfUFbSybNtKGZzJDcUcvQ/3DjQhG3/os7/8a0nYW2HggczrknuTl+LIVB1/12ciura+sb+c3C1vbO7l5x/6BhokQzXmeRjHTLp4ZLoXgdBUreijWnoS950x/dTP3mA9dGRKqG45h3QzpQIhCMopXuO8if0A/SGrWBSa9YcsvuDGSZeBkpQYZqr/jV6UcsCblCJqkxbc+NsZtSjYLZ+wqdxPCYshEd8LaliobcdNPZ1hNyYpU+CSJtj0IyU38nUhoaMw59OxlSHJpFbyr+57UTDK67qVBxglyx+UNBIglGZFoB6QvNGcqxJZRpYXclbEg1ZWiLKtgSvMUvL5PGWdm7LF/cnZcqJKsjD0dwDKfgwRVU4BaqUAcGGp7hFd6cR+fFeXc+5qM5J8scwh84nz/0R5K3</latexit> Table <latexit sha1_base64="FhdqTXgEyHAu4DrxJBiKEEnPY+4=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoMQL2E3+DoGvHiMaB6QLGF2MpsMmZ1dZnqFEPIJXjwo4tUv8ubfOEn2oIkFDUVVN91dQSKFQdf9dnJr6xubW/ntws7u3v5B8fCoaeJUM95gsYx1O6CGS6F4AwVK3k40p1EgeSsY3c781hPXRsTqEccJ9yM6UCIUjKKVHsrV816x5FbcOcgq8TJSggz1XvGr249ZGnGFTFJjOp6boD+hGgWTfFropoYnlI3ogHcsVTTixp/MT52SM6v0SRhrWwrJXP09MaGRMeMosJ0RxaFZ9mbif14nxfDGnwiVpMgVWywKU0kwJrO/SV9ozlCOLaFMC3srYUOqKUObTsGG4C2/vEqa1Yp3Vbm8vyjVSBZHHk7gFMrgwTXU4A7q0AAGA3iGV3hzpPPivDsfi9ack80cwx84nz86Ro0D</latexit> (2) <latexit sha1_base64="V7hkhScy087xDu1kVBnrqQ0tG3g=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBahXkpS/DoWvHisYGqhDWWz3bRLdzdhdyOE0N/gxYMiXv1B3vw3btsctPXBwOO9GWbmhQln2rjut1NaW9/Y3CpvV3Z29/YPqodHHR2nilCfxDxW3RBrypmkvmGG026iKBYhp4/h5HbmPz5RpVksH0yW0EDgkWQRI9hYya9ng+b5oFpzG+4caJV4BalBgfag+tUfxiQVVBrCsdY9z01MkGNlGOF0WumnmiaYTPCI9iyVWFAd5PNjp+jMKkMUxcqWNGiu/p7IsdA6E6HtFNiM9bI3E//zeqmJboKcySQ1VJLFoijlyMRo9jkaMkWJ4ZklmChmb0VkjBUmxuZTsSF4yy+vkk6z4V01Lu8vai1UxFGGEziFOnhwDS24gzb4QIDBM7zCmyOdF+fd+Vi0lpxi5hj+wPn8Ac4Aje8=</latexit> (y2) <latexit sha1_base64="tTy+M4RQrUVD6//bZUzhvxVjzwM=">AAACDXicbVC7TgMxEPTxJrwClDQWAYkqukPiUSLRUAaJPKQkivacPbDw2Sd7DxFF+QEafoWGAoRo6en4G5xHAYGpxjOzWu/EmZKOwvArmJmdm19YXFourKyurW8UN7dqzuRWYFUYZWwjBodKaqySJIWNzCKkscJ6fHs+9Ot3aJ00+op6GbZTuNYykQLIS53iXgUtJ/BxXoF747jUjkAL5Imxwwdacp1iKSyHI/C/JJqQEpug0il+trpG5ClqEgqca0ZhRu0+WJJC4aDQyh1mIG7hGpueakjRtfujawZ83yvd0frEaOIj9edEH1LnemnskynQjZv2huJ/XjOn5LTdlzrLCbUYL0pyxcnwYTW8Ky0KUj1PQFjp/8rFDVgQ5Ass+BKi6ZP/ktphOTouH10els74pI4ltsN22QGL2Ak7YxeswqpMsAf2xF7Ya/AYPAdvwfs4OhNMZrbZLwQf3wxQm3c=</latexit> Per table Paxos instance for inserts <latexit sha1_base64="MPobKWh3CKHSmHo/Nrt37+GnUEQ=">AAACE3icbVC7TsMwFHV4lvIqMLJYVEiIoUoq8RgrsTAGiT6ktqoc56a16tiR7QBV1X9g4VdYGECIlYWNv8FNM0DLmY7OuUf33hMknGnjut/O0vLK6tp6YaO4ubW9s1va229omSoKdSq5VK2AaOBMQN0ww6GVKCBxwKEZDK+mfvMOlGZS3JpRAt2Y9AWLGCXGSr3SqQ8KK6BShdgnD1JjJrQhggKOpMIC7nEe171S2a24GfAi8XJSRjn8XumrE0qaxiAM5UTrtucmpjsmyjDKYVLspBoSQoekD21LBYlBd8fZTxN8bJUwuyGSwuBM/Z0Yk1jrURzYyZiYgZ73puJ/Xjs10WV3zESSGhB0tihKOTYSTwvCIbN1GD6yhFDF7K2YDogi1NgeirYEb/7lRdKoVrzzytlNtVzDeR0FdIiO0Any0AWqoWvkozqi6BE9o1f05jw5L8678zEbXXLyzAH6A+fzB8hSngU=</latexit> Per record Paxos instance for new versions <latexit sha1_base64="oMYxLw/02fNAdOe6ji8smAxr+Mc=">AAAB7XicbVDLSgMxFL1TX7W+qi7dBIvgqswUfCwLbtxZwT6gHUomzbSxmWRIMkIZ+g9uXCji1v9x59+Ymc5CWw+EHM65l3vvCWLOtHHdb6e0tr6xuVXeruzs7u0fVA+POlomitA2kVyqXoA15UzQtmGG016sKI4CTrvB9Cbzu09UaSbFg5nF1I/wWLCQEWys1LmLs29Yrbl1NwdaJV5BalCgNax+DUaSJBEVhnCsdd9zY+OnWBlGOJ1XBommMSZTPKZ9SwWOqPbTfNs5OrPKCIVS2ScMytXfHSmOtJ5Fga2MsJnoZS8T//P6iQmv/ZSJODFUkMWgMOHISJSdjkZMUWL4zBJMFLO7IjLBChNjA6rYELzlk1dJp1H3LusX941aExVxlOEETuEcPLiCJtxCC9pA4BGe4RXeHOm8OO/Ox6K05BQ9x/AHzucPps+PFQ==</latexit> Option 6
11. アトミックコミット 1. コーディネーターはトランザクションのコミ ット時に任意の行の書き込みをオプションと してリーダーにリクエストする． ここで，各行のオプションは高々 1 つだけであ るという制約を課す． 2. 各行のリーダーは write-write コンフリクトが ないことを確認してオプションを受理する． 3. コーディネーターはすべての書き込みオプシ ョンが受理されたことを確認し，コミットを完 了する．それ以外の場合はアボートする． 4. コミットできた場合は非同期に書き込みオプ ションを確定させる． <latexit sha1_base64="nO2prTunTsglLGiKVpvuJMKbelc=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKr2PAi8cI5gHJEmZnZ5MxszvLTG8ghPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXkEph0HW/ncLa+sbmVnG7tLO7t39QPjxqGpVpxhtMSaXbATVcioQ3UKDk7VRzGgeSt4Lh3cxvjbg2QiWPOE65H9N+IiLBKFqp2R2FCk2vXHGr7hxklXg5qUCOeq/81Q0Vy2KeIJPUmI7npuhPqEbBJJ+WupnhKWVD2ucdSxMac+NP5tdOyZlVQhIpbStBMld/T0xobMw4DmxnTHFglr2Z+J/XyTC69SciSTPkCVssijJJUJHZ6yQUmjOUY0so08LeStiAasrQBlSyIXjLL6+S5kXVu65ePVxWaiSPowgncArn4MEN1OAe6tAABk/wDK/w5ijnxXl3PhatBSefOYY/cD5/AMR1jyo=</latexit> . . . <latexit sha1_base64="nO2prTunTsglLGiKVpvuJMKbelc=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKr2PAi8cI5gHJEmZnZ5MxszvLTG8ghPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXkEph0HW/ncLa+sbmVnG7tLO7t39QPjxqGpVpxhtMSaXbATVcioQ3UKDk7VRzGgeSt4Lh3cxvjbg2QiWPOE65H9N+IiLBKFqp2R2FCk2vXHGr7hxklXg5qUCOeq/81Q0Vy2KeIJPUmI7npuhPqEbBJJ+WupnhKWVD2ucdSxMac+NP5tdOyZlVQhIpbStBMld/T0xobMw4DmxnTHFglr2Z+J/XyTC69SciSTPkCVssijJJUJHZ6yQUmjOUY0so08LeStiAasrQBlSyIXjLL6+S5kXVu65ePVxWaiSPowgncArn4MEN1OAe6tAABk/wDK/w5ijnxXl3PhatBSefOYY/cD5/AMR1jyo=</latexit> . . . <latexit sha1_base64="kgzki4oKtHt8M1hCiWltT9OsVCA=">AAAB9XicbVDJSgNBEO2JW4xb1KOXxkHwFGbE7Rjw4jGCWSAzhp5OTdKkZ7G7Rg1D/sOLB0W8+i/e/Bs7y0ETHxQ83quiql6QSqHRcb6twtLyyupacb20sbm1vVPe3WvoJFMc6jyRiWoFTIMUMdRRoIRWqoBFgYRmMLga+80HUFok8S0OU/Aj1otFKDhDI915CE8YhLlna7gfdcq2U3EmoIvEnRGbzFDrlL+8bsKzCGLkkmnddp0U/ZwpFFzCqORlGlLGB6wHbUNjFoH288nVI3pklC4NE2UqRjpRf0/kLNJ6GAWmM2LY1/PeWPzPa2cYXvq5iNMMIebTRWEmKSZ0HAHtCgUc5dAQxpUwt1LeZ4pxNEGVTAju/MuLpHFScc8rZzendpXO4iiSA3JIjolLLkiVXJMaqRNOFHkmr+TNerRerHfrY9pasGYz++QPrM8fwyiSlw==</latexit> #seq <latexit 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sha1_base64="FhdqTXgEyHAu4DrxJBiKEEnPY+4=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoMQL2E3+DoGvHiMaB6QLGF2MpsMmZ1dZnqFEPIJXjwo4tUv8ubfOEn2oIkFDUVVN91dQSKFQdf9dnJr6xubW/ntws7u3v5B8fCoaeJUM95gsYx1O6CGS6F4AwVK3k40p1EgeSsY3c781hPXRsTqEccJ9yM6UCIUjKKVHsrV816x5FbcOcgq8TJSggz1XvGr249ZGnGFTFJjOp6boD+hGgWTfFropoYnlI3ogHcsVTTixp/MT52SM6v0SRhrWwrJXP09MaGRMeMosJ0RxaFZ9mbif14nxfDGnwiVpMgVWywKU0kwJrO/SV9ozlCOLaFMC3srYUOqKUObTsGG4C2/vEqa1Yp3Vbm8vyjVSBZHHk7gFMrgwTXU4A7q0AAGA3iGV3hzpPPivDsfi9ack80cwx84nz86Ro0D</latexit> (2) <latexit sha1_base64="V7hkhScy087xDu1kVBnrqQ0tG3g=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBahXkpS/DoWvHisYGqhDWWz3bRLdzdhdyOE0N/gxYMiXv1B3vw3btsctPXBwOO9GWbmhQln2rjut1NaW9/Y3CpvV3Z29/YPqodHHR2nilCfxDxW3RBrypmkvmGG026iKBYhp4/h5HbmPz5RpVksH0yW0EDgkWQRI9hYya9ng+b5oFpzG+4caJV4BalBgfag+tUfxiQVVBrCsdY9z01MkGNlGOF0WumnmiaYTPCI9iyVWFAd5PNjp+jMKkMUxcqWNGiu/p7IsdA6E6HtFNiM9bI3E//zeqmJboKcySQ1VJLFoijlyMRo9jkaMkWJ4ZklmChmb0VkjBUmxuZTsSF4yy+vkk6z4V01Lu8vai1UxFGGEziFOnhwDS24gzb4QIDBM7zCmyOdF+fd+Vi0lpxi5hj+wPn8Ac4Aje8=</latexit> (y2) <latexit sha1_base64="tTy+M4RQrUVD6//bZUzhvxVjzwM=">AAACDXicbVC7TgMxEPTxJrwClDQWAYkqukPiUSLRUAaJPKQkivacPbDw2Sd7DxFF+QEafoWGAoRo6en4G5xHAYGpxjOzWu/EmZKOwvArmJmdm19YXFourKyurW8UN7dqzuRWYFUYZWwjBodKaqySJIWNzCKkscJ6fHs+9Ot3aJ00+op6GbZTuNYykQLIS53iXgUtJ/BxXoF747jUjkAL5Imxwwdacp1iKSyHI/C/JJqQEpug0il+trpG5ClqEgqca0ZhRu0+WJJC4aDQyh1mIG7hGpueakjRtfujawZ83yvd0frEaOIj9edEH1LnemnskynQjZv2huJ/XjOn5LTdlzrLCbUYL0pyxcnwYTW8Ky0KUj1PQFjp/8rFDVgQ5Ass+BKi6ZP/ktphOTouH10els74pI4ltsN22QGL2Ak7YxeswqpMsAf2xF7Ya/AYPAdvwfs4OhNMZrbZLwQf3wxQm3c=</latexit> Per table Paxos instance for inserts <latexit sha1_base64="MPobKWh3CKHSmHo/Nrt37+GnUEQ=">AAACE3icbVC7TsMwFHV4lvIqMLJYVEiIoUoq8RgrsTAGiT6ktqoc56a16tiR7QBV1X9g4VdYGECIlYWNv8FNM0DLmY7OuUf33hMknGnjut/O0vLK6tp6YaO4ubW9s1va229omSoKdSq5VK2AaOBMQN0ww6GVKCBxwKEZDK+mfvMOlGZS3JpRAt2Y9AWLGCXGSr3SqQ8KK6BShdgnD1JjJrQhggKOpMIC7nEe171S2a24GfAi8XJSRjn8XumrE0qaxiAM5UTrtucmpjsmyjDKYVLspBoSQoekD21LBYlBd8fZTxN8bJUwuyGSwuBM/Z0Yk1jrURzYyZiYgZ73puJ/Xjs10WV3zESSGhB0tihKOTYSTwvCIbN1GD6yhFDF7K2YDogi1NgeirYEb/7lRdKoVrzzytlNtVzDeR0FdIiO0Any0AWqoWvkozqi6BE9o1f05jw5L8678zEbXXLyzAH6A+fzB8hSngU=</latexit> Per record Paxos instance for new versions <latexit sha1_base64="oMYxLw/02fNAdOe6ji8smAxr+Mc=">AAAB7XicbVDLSgMxFL1TX7W+qi7dBIvgqswUfCwLbtxZwT6gHUomzbSxmWRIMkIZ+g9uXCji1v9x59+Ymc5CWw+EHM65l3vvCWLOtHHdb6e0tr6xuVXeruzs7u0fVA+POlomitA2kVyqXoA15UzQtmGG016sKI4CTrvB9Cbzu09UaSbFg5nF1I/wWLCQEWys1LmLs29Yrbl1NwdaJV5BalCgNax+DUaSJBEVhnCsdd9zY+OnWBlGOJ1XBommMSZTPKZ9SwWOqPbTfNs5OrPKCIVS2ScMytXfHSmOtJ5Fga2MsJnoZS8T//P6iQmv/ZSJODFUkMWgMOHISJSdjkZMUWL4zBJMFLO7IjLBChNjA6rYELzlk1dJp1H3LusX941aExVxlOEETuEcPLiCJtxCC9pA4BGe4RXeHOm8OO/Ox6K05BQ9x/AHzucPps+PFQ==</latexit> Option 7
12. Write-write コンフリクトの検出 1. コーディネーターはトランザクションのコミ ット時に write セットを読み取り，読み取った バージョンを vread として書き込みオプション vread → vwrite をリーダーに送信する． 2. リーダーは行の最新のバージョンと書き込み リクエストの vread が一致する場合，書き込み オプションを受理する． それ以外の場合は別のトランザクションが行 を書き換えている (write-write コンフリクト) ため，書き込みオプションを却下する． <latexit sha1_base64="nO2prTunTsglLGiKVpvuJMKbelc=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKr2PAi8cI5gHJEmZnZ5MxszvLTG8ghPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXkEph0HW/ncLa+sbmVnG7tLO7t39QPjxqGpVpxhtMSaXbATVcioQ3UKDk7VRzGgeSt4Lh3cxvjbg2QiWPOE65H9N+IiLBKFqp2R2FCk2vXHGr7hxklXg5qUCOeq/81Q0Vy2KeIJPUmI7npuhPqEbBJJ+WupnhKWVD2ucdSxMac+NP5tdOyZlVQhIpbStBMld/T0xobMw4DmxnTHFglr2Z+J/XyTC69SciSTPkCVssijJJUJHZ6yQUmjOUY0so08LeStiAasrQBlSyIXjLL6+S5kXVu65ePVxWaiSPowgncArn4MEN1OAe6tAABk/wDK/w5ijnxXl3PhatBSefOYY/cD5/AMR1jyo=</latexit> . . . <latexit sha1_base64="nO2prTunTsglLGiKVpvuJMKbelc=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKr2PAi8cI5gHJEmZnZ5MxszvLTG8ghPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXkEph0HW/ncLa+sbmVnG7tLO7t39QPjxqGpVpxhtMSaXbATVcioQ3UKDk7VRzGgeSt4Lh3cxvjbg2QiWPOE65H9N+IiLBKFqp2R2FCk2vXHGr7hxklXg5qUCOeq/81Q0Vy2KeIJPUmI7npuhPqEbBJJ+WupnhKWVD2ucdSxMac+NP5tdOyZlVQhIpbStBMld/T0xobMw4DmxnTHFglr2Z+J/XyTC69SciSTPkCVssijJJUJHZ6yQUmjOUY0so08LeStiAasrQBlSyIXjLL6+S5kXVu65ePVxWaiSPowgncArn4MEN1OAe6tAABk/wDK/w5ijnxXl3PhatBSefOYY/cD5/AMR1jyo=</latexit> . . . <latexit sha1_base64="kgzki4oKtHt8M1hCiWltT9OsVCA=">AAAB9XicbVDJSgNBEO2JW4xb1KOXxkHwFGbE7Rjw4jGCWSAzhp5OTdKkZ7G7Rg1D/sOLB0W8+i/e/Bs7y0ETHxQ83quiql6QSqHRcb6twtLyyupacb20sbm1vVPe3WvoJFMc6jyRiWoFTIMUMdRRoIRWqoBFgYRmMLga+80HUFok8S0OU/Aj1otFKDhDI915CE8YhLlna7gfdcq2U3EmoIvEnRGbzFDrlL+8bsKzCGLkkmnddp0U/ZwpFFzCqORlGlLGB6wHbUNjFoH288nVI3pklC4NE2UqRjpRf0/kLNJ6GAWmM2LY1/PeWPzPa2cYXvq5iNMMIebTRWEmKSZ0HAHtCgUc5dAQxpUwt1LeZ4pxNEGVTAju/MuLpHFScc8rZzendpXO4iiSA3JIjolLLkiVXJMaqRNOFHkmr+TNerRerHfrY9pasGYz++QPrM8fwyiSlw==</latexit> #seq <latexit sha1_base64="kgzki4oKtHt8M1hCiWltT9OsVCA=">AAAB9XicbVDJSgNBEO2JW4xb1KOXxkHwFGbE7Rjw4jGCWSAzhp5OTdKkZ7G7Rg1D/sOLB0W8+i/e/Bs7y0ETHxQ83quiql6QSqHRcb6twtLyyupacb20sbm1vVPe3WvoJFMc6jyRiWoFTIMUMdRRoIRWqoBFgYRmMLga+80HUFok8S0OU/Aj1otFKDhDI915CE8YhLlna7gfdcq2U3EmoIvEnRGbzFDrlL+8bsKzCGLkkmnddp0U/ZwpFFzCqORlGlLGB6wHbUNjFoH288nVI3pklC4NE2UqRjpRf0/kLNJ6GAWmM2LY1/PeWPzPa2cYXvq5iNMMIebTRWEmKSZ0HAHtCgUc5dAQxpUwt1LeZ4pxNEGVTAju/MuLpHFScc8rZzendpXO4iiSA3JIjolLLkiVXJMaqRNOFHkmr+TNerRerHfrY9pasGYz++QPrM8fwyiSlw==</latexit> #seq <latexit sha1_base64="qFe8eHt4608FxZojNKqV6PnoGec=">AAAB+HicbVDLSsNAFJ34rPXRqEs3g0VwVRLxtSy4cVnBPqANZTKZtEMnM2HmRqyhX+LGhSJu/RR3/o3TNgttPXDhcM693HtPmApuwPO+nZXVtfWNzdJWeXtnd6/i7h+0jMo0ZU2qhNKdkBgmuGRN4CBYJ9WMJKFg7XB0M/XbD0wbruQ9jFMWJGQgecwpASv13UoP2COEca4ZVTqa9N2qV/NmwMvEL0gVFWj03a9epGiWMAlUEGO6vpdCkBMNnAo2Kfcyw1JCR2TAupZKkjAT5LPDJ/jEKhGOlbYlAc/U3xM5SYwZJ6HtTAgMzaI3Ff/zuhnE10HOZZoBk3S+KM4EBoWnKeCI239BjC0hVHN7K6ZDogkFm1XZhuAvvrxMWmc1/7J2cXdereMijhI6QsfoFPnoCtXRLWqgJqIoQ8/oFb05T86L8+58zFtXnGLmEP2B8/kDfJOTiQ==</latexit> record <latexit sha1_base64="LWRGAY1AzR9cg9mexPTnmyEKhW0=">AAAB83icbVDLSsNAFJ3UV62vqks3g0VwVRLxtSy4cVnB1kITymR60w6dTMLMjVhCf8ONC0Xc+jPu/BunbRbaemDgcM653DsnTKUw6LrfTmlldW19o7xZ2dre2d2r7h+0TZJpDi2eyER3QmZACgUtFCihk2pgcSjhIRzdTP2HR9BGJOoexykEMRsoEQnO0Eq+j/CEYZTbyKRXrbl1dwa6TLyC1EiBZq/65fcTnsWgkEtmTNdzUwxyplFwCZOKnxlIGR+xAXQtVSwGE+Szmyf0xCp9GiXaPoV0pv6eyFlszDgObTJmODSL3lT8z+tmGF0HuVBphqD4fFGUSYoJnRZA+0IDRzm2hHEt7K2UD5lmHG1NFVuCt/jlZdI+q3uX9Yu781qDFnWUyRE5JqfEI1ekQW5Jk7QIJyl5Jq/kzcmcF+fd+ZhHS04xc0j+wPn8AbWhkgg=</latexit> ver <latexit sha1_base64="fpOUP9RYMQm+quQM2279uiBCeU4=">AAAB6HicbVDLSgNBEOyNrxhfUY9eBoPgKeyKr2PAi8cEzAOSJcxOepMxs7PLzKwQlnyBFw+KePWTvPk3TpI9aGJBQ1HVTXdXkAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4bua3n1BpHssHM0nQj+hQ8pAzaqzU8Prlilt15yCrxMtJBXLU++Wv3iBmaYTSMEG17npuYvyMKsOZwGmpl2pMKBvTIXYtlTRC7WfzQ6fkzCoDEsbKljRkrv6eyGik9SQKbGdEzUgvezPxP6+bmvDWz7hMUoOSLRaFqSAmJrOvyYArZEZMLKFMcXsrYSOqKDM2m5INwVt+eZW0LqredfWqcVmpkTyOIpzAKZyDBzdQg3uoQxMYIDzDK7w5j86L8+58LFoLTj5zDH/gfP4Ac6OMnQ==</latexit> 1 <latexit sha1_base64="LhbXp3uCHkPMg8o4VBNTeuY+z8w=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0mKX8eCF48t2FpoQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgpr6xubW8Xt0s7u3v5B+fCoreNUMWyxWMSqE1CNgktsGW4EdhKFNAoEPgTj25n/8IRK81jem0mCfkSHkoecUWOlZq1frrhVdw6ySrycVCBHo1/+6g1ilkYoDRNU667nJsbPqDKcCZyWeqnGhLIxHWLXUkkj1H42P3RKzqwyIGGsbElD5urviYxGWk+iwHZG1Iz0sjcT//O6qQlv/IzLJDUo2WJRmApiYjL7mgy4QmbExBLKFLe3EjaiijJjsynZELzll1dJu1b1rqqXzYtKneRxFOEETuEcPLiGOtxBA1rAAOEZXuHNeXRenHfnY9FacPKZY/gD5/MHdSeMng==</latexit> 2 <latexit sha1_base64="7aVD/pKsk/NifnUckehPLDVIAkk=">AAAB6HicbVDLSgNBEOz1GeMr6tHLYBA8hV3fx4AXjwmYByRLmJ30JmNmZ5eZWSEs+QIvHhTx6id582+cJHvQxIKGoqqb7q4gEVwb1/12VlbX1jc2C1vF7Z3dvf3SwWFTx6li2GCxiFU7oBoFl9gw3AhsJwppFAhsBaO7qd96QqV5LB/MOEE/ogPJQ86osVL9olcquxV3BrJMvJyUIUetV/rq9mOWRigNE1Trjucmxs+oMpwJnBS7qcaEshEdYMdSSSPUfjY7dEJOrdInYaxsSUNm6u+JjEZaj6PAdkbUDPWiNxX/8zqpCW/9jMskNSjZfFGYCmJiMv2a9LlCZsTYEsoUt7cSNqSKMmOzKdoQvMWXl0nzvOJdV67ql+UqyeMowDGcwBl4cANVuIcaNIABwjO8wpvz6Lw4787HvHXFyWeO4A+czx92q4yf</latexit> 3 <latexit sha1_base64="MTZ6hKSdEqhWYpwl4KRPrCBQZXI=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKr2PAi8eI5gHJEmYnvcmQ2dllZlYMSz7BiwdFvPpF3vwbJ8keNLGgoajqprsrSATXxnW/ncLK6tr6RnGztLW9s7tX3j9o6jhVDBssFrFqB1Sj4BIbhhuB7UQhjQKBrWB0M/Vbj6g0j+WDGSfoR3QgecgZNVa6f+p5vXLFrbozkGXi5aQCOeq98le3H7M0QmmYoFp3PDcxfkaV4UzgpNRNNSaUjegAO5ZKGqH2s9mpE3JilT4JY2VLGjJTf09kNNJ6HAW2M6JmqBe9qfif10lNeO1nXCapQcnmi8JUEBOT6d+kzxUyI8aWUKa4vZWwIVWUGZtOyYbgLb68TJpnVe+yenF3XqmRPI4iHMExnIIHV1CDW6hDAxgM4Ble4c0Rzovz7nzMWwtOPnMIf+B8/gAEto2I</latexit> x1 <latexit sha1_base64="YBmdHHJkVqPpSkOypWwanD4AMfw=">AAAB6nicbVDLSgNBEOz1GeMr6tHLYBA8hd3g6xjw4jGieUCyhNnJbDJkdnaZ6RXDkk/w4kERr36RN//GSbIHTSxoKKq66e4KEikMuu63s7K6tr6xWdgqbu/s7u2XDg6bJk414w0Wy1i3A2q4FIo3UKDk7URzGgWSt4LRzdRvPXJtRKwecJxwP6IDJULBKFrp/qlX7ZXKbsWdgSwTLydlyFHvlb66/ZilEVfIJDWm47kJ+hnVKJjkk2I3NTyhbEQHvGOpohE3fjY7dUJOrdInYaxtKSQz9fdERiNjxlFgOyOKQ7PoTcX/vE6K4bWfCZWkyBWbLwpTSTAm079JX2jOUI4toUwLeythQ6opQ5tO0YbgLb68TJrVindZubg7L9dIHkcBjuEEzsCDK6jBLdShAQwG8Ayv8OZI58V5dz7mrStOPnMEf+B8/gAGOo2J</latexit> x2 <latexit sha1_base64="E5s6i2ii+Knmtz5KDQaUgXM0/Hg=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKez6Pga8eIxoHpAsYXbSmwyZnV1mZsWw5BO8eFDEq1/kzb9xkuxBowUNRVU33V1BIrg2rvvlFJaWV1bXiuuljc2t7Z3y7l5Tx6li2GCxiFU7oBoFl9gw3AhsJwppFAhsBaPrqd96QKV5LO/NOEE/ogPJQ86osdLdY++0V664VXcG8pd4OalAjnqv/NntxyyNUBomqNYdz02Mn1FlOBM4KXVTjQllIzrAjqWSRqj9bHbqhBxZpU/CWNmShszUnxMZjbQeR4HtjKgZ6kVvKv7ndVITXvkZl0lqULL5ojAVxMRk+jfpc4XMiLEllClubyVsSBVlxqZTsiF4iy//Jc2TqndRPb89q9RIHkcRDuAQjsGDS6jBDdShAQwG8AQv8OoI59l5c97nrQUnn9mHX3A+vgEHvo2K</latexit> x3 <latexit 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sha1_base64="fpOUP9RYMQm+quQM2279uiBCeU4=">AAAB6HicbVDLSgNBEOyNrxhfUY9eBoPgKeyKr2PAi8cEzAOSJcxOepMxs7PLzKwQlnyBFw+KePWTvPk3TpI9aGJBQ1HVTXdXkAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4bua3n1BpHssHM0nQj+hQ8pAzaqzU8Prlilt15yCrxMtJBXLU++Wv3iBmaYTSMEG17npuYvyMKsOZwGmpl2pMKBvTIXYtlTRC7WfzQ6fkzCoDEsbKljRkrv6eyGik9SQKbGdEzUgvezPxP6+bmvDWz7hMUoOSLRaFqSAmJrOvyYArZEZMLKFMcXsrYSOqKDM2m5INwVt+eZW0LqredfWqcVmpkTyOIpzAKZyDBzdQg3uoQxMYIDzDK7w5j86L8+58LFoLTj5zDH/gfP4Ac6OMnQ==</latexit> 1 <latexit 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sha1_base64="kgzki4oKtHt8M1hCiWltT9OsVCA=">AAAB9XicbVDJSgNBEO2JW4xb1KOXxkHwFGbE7Rjw4jGCWSAzhp5OTdKkZ7G7Rg1D/sOLB0W8+i/e/Bs7y0ETHxQ83quiql6QSqHRcb6twtLyyupacb20sbm1vVPe3WvoJFMc6jyRiWoFTIMUMdRRoIRWqoBFgYRmMLga+80HUFok8S0OU/Aj1otFKDhDI915CE8YhLlna7gfdcq2U3EmoIvEnRGbzFDrlL+8bsKzCGLkkmnddp0U/ZwpFFzCqORlGlLGB6wHbUNjFoH288nVI3pklC4NE2UqRjpRf0/kLNJ6GAWmM2LY1/PeWPzPa2cYXvq5iNMMIebTRWEmKSZ0HAHtCgUc5dAQxpUwt1LeZ4pxNEGVTAju/MuLpHFScc8rZzendpXO4iiSA3JIjolLLkiVXJMaqRNOFHkmr+TNerRerHfrY9pasGYz++QPrM8fwyiSlw==</latexit> #seq <latexit sha1_base64="LWRGAY1AzR9cg9mexPTnmyEKhW0=">AAAB83icbVDLSsNAFJ3UV62vqks3g0VwVRLxtSy4cVnB1kITymR60w6dTMLMjVhCf8ONC0Xc+jPu/BunbRbaemDgcM653DsnTKUw6LrfTmlldW19o7xZ2dre2d2r7h+0TZJpDi2eyER3QmZACgUtFCihk2pgcSjhIRzdTP2HR9BGJOoexykEMRsoEQnO0Eq+j/CEYZTbyKRXrbl1dwa6TLyC1EiBZq/65fcTnsWgkEtmTNdzUwxyplFwCZOKnxlIGR+xAXQtVSwGE+Szmyf0xCp9GiXaPoV0pv6eyFlszDgObTJmODSL3lT8z+tmGF0HuVBphqD4fFGUSYoJnRZA+0IDRzm2hHEt7K2UD5lmHG1NFVuCt/jlZdI+q3uX9Yu781qDFnWUyRE5JqfEI1ekQW5Jk7QIJyl5Jq/kzcmcF+fd+ZhHS04xc0j+wPn8AbWhkgg=</latexit> ver <latexit sha1_base64="DUTHrYsSDUSGIHVIePsEn4U8J2s=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0nEr2PBi8eK1hbaUDbbTbt0swm7EyGE/gQvHhTx6i/y5r9x2+agrQ8GHu/NMDMvSKQw6LrfTmlldW19o7xZ2dre2d2r7h88mjjVjLdYLGPdCajhUijeQoGSdxLNaRRI3g7GN1O//cS1EbF6wCzhfkSHSoSCUbTSfdZ3+9WaW3dnIMvEK0gNCjT71a/eIGZpxBUySY3pem6Cfk41Cib5pNJLDU8oG9Mh71qqaMSNn89OnZATqwxIGGtbCslM/T2R08iYLApsZ0RxZBa9qfif100xvPZzoZIUuWLzRWEqCcZk+jcZCM0ZyswSyrSwtxI2opoytOlUbAje4svL5PGs7l3WL+7Oaw1SxFGGIziGU/DgChpwC01oAYMhPMMrvDnSeXHenY95a8kpZg7hD5zPHwS4jYg=</latexit> y0 <latexit sha1_base64="DJZMiTQxnl+dH+IcO58zRU/sfCQ=">AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0nEr2PBi8eK1hbaUDbbTbt0swm7EyGE/gQvHhTx6i/y5r9x2+agrQ8GHu/NMDMvSKQw6LrfTmlldW19o7xZ2dre2d2r7h88mjjVjLdYLGPdCajhUijeQoGSdxLNaRRI3g7GN1O//cS1EbF6wCzhfkSHSoSCUbTSfdb3+tWaW3dnIMvEK0gNCjT71a/eIGZpxBUySY3pem6Cfk41Cib5pNJLDU8oG9Mh71qqaMSNn89OnZATqwxIGGtbCslM/T2R08iYLApsZ0RxZBa9qfif100xvPZzoZIUuWLzRWEqCcZk+jcZCM0ZyswSyrSwtxI2opoytOlUbAje4svL5PGs7l3WL+7Oaw1SxFGGIziGU/DgChpwC01oAYMhPMMrvDnSeXHenY95a8kpZg7hD5zPHwY8jYk=</latexit> y1 <latexit sha1_base64="fpOUP9RYMQm+quQM2279uiBCeU4=">AAAB6HicbVDLSgNBEOyNrxhfUY9eBoPgKeyKr2PAi8cEzAOSJcxOepMxs7PLzKwQlnyBFw+KePWTvPk3TpI9aGJBQ1HVTXdXkAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4bua3n1BpHssHM0nQj+hQ8pAzaqzU8Prlilt15yCrxMtJBXLU++Wv3iBmaYTSMEG17npuYvyMKsOZwGmpl2pMKBvTIXYtlTRC7WfzQ6fkzCoDEsbKljRkrv6eyGik9SQKbGdEzUgvezPxP6+bmvDWz7hMUoOSLRaFqSAmJrOvyYArZEZMLKFMcXsrYSOqKDM2m5INwVt+eZW0LqredfWqcVmpkTyOIpzAKZyDBzdQg3uoQxMYIDzDK7w5j86L8+58LFoLTj5zDH/gfP4Ac6OMnQ==</latexit> 1 <latexit sha1_base64="pIVZpONp5sw1Q3+T+sIzrzjkUl4=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoPgKeyKr2PAi8eI5gHJEmYns8mQ2dllpleISz7BiwdFvPpF3vwbJ8keNLGgoajqprsrSKQw6LrfTmFldW19o7hZ2tre2d0r7x80TZxqxhsslrFuB9RwKRRvoEDJ24nmNAokbwWjm6nfeuTaiFg94DjhfkQHSoSCUbTS/VPP7ZUrbtWdgSwTLycVyFHvlb+6/ZilEVfIJDWm47kJ+hnVKJjkk1I3NTyhbEQHvGOpohE3fjY7dUJOrNInYaxtKSQz9fdERiNjxlFgOyOKQ7PoTcX/vE6K4bWfCZWkyBWbLwpTSTAm079JX2jOUI4toUwLeythQ6opQ5tOyYbgLb68TJpnVe+yenF3XqmRPI4iHMExnIIHV1CDW6hDAxgM4Ble4c2Rzovz7nzMWwtOPnMIf+B8/gAGPo2J</latexit> z0 <latexit sha1_base64="rLm8TD39zMcSFK0UVqXvleVg06A=">AAAB9XicbVDLSgMxFL1TX7W+qi7dBIvgqsyIr2XBjcsKfUFbSybNtKGZzJDcUcvQ/3DjQhG3/os7/8a0nYW2HggczrknuTl+LIVB1/12ciura+sb+c3C1vbO7l5x/6BhokQzXmeRjHTLp4ZLoXgdBUreijWnoS950x/dTP3mA9dGRKqG45h3QzpQIhCMopXuO8if0A/SGrWBSa9YcsvuDGSZeBkpQYZqr/jV6UcsCblCJqkxbc+NsZtSjYLZ+wqdxPCYshEd8LaliobcdNPZ1hNyYpU+CSJtj0IyU38nUhoaMw59OxlSHJpFbyr+57UTDK67qVBxglyx+UNBIglGZFoB6QvNGcqxJZRpYXclbEg1ZWiLKtgSvMUvL5PGWdm7LF/cnZcqJKsjD0dwDKfgwRVU4BaqUAcGGp7hFd6cR+fFeXc+5qM5J8scwh84nz/0R5K3</latexit> Table <latexit sha1_base64="FhdqTXgEyHAu4DrxJBiKEEnPY+4=">AAAB6nicbVDLSgNBEOyNrxhfUY9eBoMQL2E3+DoGvHiMaB6QLGF2MpsMmZ1dZnqFEPIJXjwo4tUv8ubfOEn2oIkFDUVVN91dQSKFQdf9dnJr6xubW/ntws7u3v5B8fCoaeJUM95gsYx1O6CGS6F4AwVK3k40p1EgeSsY3c781hPXRsTqEccJ9yM6UCIUjKKVHsrV816x5FbcOcgq8TJSggz1XvGr249ZGnGFTFJjOp6boD+hGgWTfFropoYnlI3ogHcsVTTixp/MT52SM6v0SRhrWwrJXP09MaGRMeMosJ0RxaFZ9mbif14nxfDGnwiVpMgVWywKU0kwJrO/SV9ozlCOLaFMC3srYUOqKUObTsGG4C2/vEqa1Yp3Vbm8vyjVSBZHHk7gFMrgwTXU4A7q0AAGA3iGV3hzpPPivDsfi9ack80cwx84nz86Ro0D</latexit> (2) <latexit sha1_base64="V7hkhScy087xDu1kVBnrqQ0tG3g=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBahXkpS/DoWvHisYGqhDWWz3bRLdzdhdyOE0N/gxYMiXv1B3vw3btsctPXBwOO9GWbmhQln2rjut1NaW9/Y3CpvV3Z29/YPqodHHR2nilCfxDxW3RBrypmkvmGG026iKBYhp4/h5HbmPz5RpVksH0yW0EDgkWQRI9hYya9ng+b5oFpzG+4caJV4BalBgfag+tUfxiQVVBrCsdY9z01MkGNlGOF0WumnmiaYTPCI9iyVWFAd5PNjp+jMKkMUxcqWNGiu/p7IsdA6E6HtFNiM9bI3E//zeqmJboKcySQ1VJLFoijlyMRo9jkaMkWJ4ZklmChmb0VkjBUmxuZTsSF4yy+vkk6z4V01Lu8vai1UxFGGEziFOnhwDS24gzb4QIDBM7zCmyOdF+fd+Vi0lpxi5hj+wPn8Ac4Aje8=</latexit> (y2) <latexit sha1_base64="tTy+M4RQrUVD6//bZUzhvxVjzwM=">AAACDXicbVC7TgMxEPTxJrwClDQWAYkqukPiUSLRUAaJPKQkivacPbDw2Sd7DxFF+QEafoWGAoRo6en4G5xHAYGpxjOzWu/EmZKOwvArmJmdm19YXFourKyurW8UN7dqzuRWYFUYZWwjBodKaqySJIWNzCKkscJ6fHs+9Ot3aJ00+op6GbZTuNYykQLIS53iXgUtJ/BxXoF747jUjkAL5Imxwwdacp1iKSyHI/C/JJqQEpug0il+trpG5ClqEgqca0ZhRu0+WJJC4aDQyh1mIG7hGpueakjRtfujawZ83yvd0frEaOIj9edEH1LnemnskynQjZv2huJ/XjOn5LTdlzrLCbUYL0pyxcnwYTW8Ky0KUj1PQFjp/8rFDVgQ5Ass+BKi6ZP/ktphOTouH10els74pI4ltsN22QGL2Ak7YxeswqpMsAf2xF7Ya/AYPAdvwfs4OhNMZrbZLwQf3wxQm3c=</latexit> Per table Paxos instance for inserts <latexit sha1_base64="MPobKWh3CKHSmHo/Nrt37+GnUEQ=">AAACE3icbVC7TsMwFHV4lvIqMLJYVEiIoUoq8RgrsTAGiT6ktqoc56a16tiR7QBV1X9g4VdYGECIlYWNv8FNM0DLmY7OuUf33hMknGnjut/O0vLK6tp6YaO4ubW9s1va229omSoKdSq5VK2AaOBMQN0ww6GVKCBxwKEZDK+mfvMOlGZS3JpRAt2Y9AWLGCXGSr3SqQ8KK6BShdgnD1JjJrQhggKOpMIC7nEe171S2a24GfAi8XJSRjn8XumrE0qaxiAM5UTrtucmpjsmyjDKYVLspBoSQoekD21LBYlBd8fZTxN8bJUwuyGSwuBM/Z0Yk1jrURzYyZiYgZ73puJ/Xjs10WV3zESSGhB0tihKOTYSTwvCIbN1GD6yhFDF7K2YDogi1NgeirYEb/7lRdKoVrzzytlNtVzDeR0FdIiO0Any0AWqoWvkozqi6BE9o1f05jw5L8678zEbXXLyzAH6A+fzB8hSngU=</latexit> Per record Paxos instance for new versions <latexit sha1_base64="oMYxLw/02fNAdOe6ji8smAxr+Mc=">AAAB7XicbVDLSgMxFL1TX7W+qi7dBIvgqswUfCwLbtxZwT6gHUomzbSxmWRIMkIZ+g9uXCji1v9x59+Ymc5CWw+EHM65l3vvCWLOtHHdb6e0tr6xuVXeruzs7u0fVA+POlomitA2kVyqXoA15UzQtmGG016sKI4CTrvB9Cbzu09UaSbFg5nF1I/wWLCQEWys1LmLs29Yrbl1NwdaJV5BalCgNax+DUaSJBEVhnCsdd9zY+OnWBlGOJ1XBommMSZTPKZ9SwWOqPbTfNs5OrPKCIVS2ScMytXfHSmOtJ5Fga2MsJnoZS8T//P6iQmv/ZSJODFUkMWgMOHISJSdjkZMUWL4zBJMFLO7IjLBChNjA6rYELzlk1dJp1H3LusX941aExVxlOEETuEcPLiCJtxCC9pA4BGe4RXeHOm8OO/Ox6K05BQ9x/AHzucPps+PFQ==</latexit> Option 8
13. 高速クォーラムと可換性を用いた最適化 • Fast Paxos [5] に基づいて，高速クォーラムを用いた 1 RTT でのコミットを試みる． • コーディネーターがリーダーを介さず直接ストレージノードにオプションを提案でき るようになる (マスターバイパス)． • 提案が衝突した場合は，リーダーを用いてリカバリーする必要がある． • Generalized Paxos [6] に基づいて，可換なコマンドのオプションについてはそれらの集合 (CStruct) に対する合意の形成を試みる． • 書き込む値を直接指定する代わりに Decrement(col, n) のようなコマンドで値の更新を 表現することでコマンドの可換性を定義する． • 可換なコマンドを同時に受理可能にする (全順序付けを不要にする) ことで，提案の衝 突が低減され，高速パスの利用率を向上させることができる． • ただし，属性にドメイン制約がある場合に問題が生じる． 9
14. MDCC のメッセージフロー 1. コーディネーターは，任意の書き込みに ついてストレージノードに直接オプショ ンを提案し，(複数の) 可換なオプション を加えた CStruct を高速クォーラムで受理 するよう試みる (1 RTT)． 2. 高速クォーラムで受理されなかったオプ ションについて，リーダーにリカバリー の開始をリクエストし，通常クォーラム での受理を試みる (+2–2.5 RTT)． 3. すべてのオプションが受理されるとコミ ットとなる． <latexit sha1_base64="yPmVkw2Pd9xeykxpGhw9j/9O9cw=">AAAB8nicbVDLSgNBEOz1GeMr6tHLYBA8hd2Aj2MgF48RzAOSJcxOJsmQ2ZllplcISz7DiwdFvPo13vwbJ8keNLGgoajqprsrSqSw6Pvf3sbm1vbObmGvuH9weHRcOjltWZ0axptMS206EbVcCsWbKFDyTmI4jSPJ29GkPvfbT9xYodUjThMexnSkxFAwik7q1rU2A6EoatMvlf2KvwBZJ0FOypCj0S999QaapTFXyCS1thv4CYYZNSiY5LNiL7U8oWxCR7zrqKIxt2G2OHlGLp0yIENtXCkkC/X3REZja6dx5DpjimO76s3F/7xuisO7MBMqSZErtlw0TCVBTeb/k4EwnKGcOkKZEe5WwsbUUIYupaILIVh9eZ20qpXgpnL9UC3XSB5HAc7hAq4ggFuowT00oAkMNDzDK7x56L14797HsnXDy2fO4A+8zx+IO5FS</latexit> Coordinator <latexit 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sha1_base64="fWT8vlnMtuVyi/U1SqKT8kGwGPQ=">AAACDHicbVC7SgNBFL3r2/iKWgoyKIKFhF3BRynYWEYxKmSDzE5u4uDszDJzVwxLSgsbf8XGQhFbP8DOb/AnnCQWvg4MHM45lzv3JJmSjsLwPRgaHhkdG5+YLE1Nz8zOlecXTpzJrcCaMMrYs4Q7VFJjjSQpPMss8jRReJpc7vf80yu0Thp9TJ0MGylva9mSgpOXzsurseK6rZDFhNfkRFG1JjMOuxvsisW27/lUWAn7YH9J9EVW9+Dw42b58ah6Xn6Lm0bkKWoSijtXj8KMGgW3JIXCbinOHWZcXPI21j3VPEXXKPrHdNmaV5qsZax/mlhf/T5R8NS5Tpr4ZMrpwv32euJ/Xj2n1m6jkDrLCbUYLGrlipFhvWZYU1oUpDqecGGl/ysTF9xyQb6/ki8h+n3yX3KyWYm2K1uHvg0GA0zAEqzAOkSwA3twAFWogYBbuIdHeArugofgOXgZRIeCr5lF+IHg9RMnWJ6T</latexit> hPropose, vi <latexit sha1_base64="ByFon6CIN4SCzhOJf/+EyKSDeXc=">AAACDHicbVC9SjNBFL3rv/EvainI8IlgIWFX8KcUbCyjGBWyQWYnN3FwdmaZuauGJaWFja9iY6GIrQ9g5zP4Ek4SCz/1wMDhnHO5c0+SKekoDN+DoeGR0bHxicnS1PTM7Fx5fuHYmdwKrAmjjD1NuEMlNdZIksLTzCJPE4UnycVezz+5ROuk0UfUybCR8raWLSk4eemsvBIrrtsKWUx4TU4UVWsy47C7zq5YbPueT4WVsA/2m0RfZGUXDj5ulh8Pq2flt7hpRJ6iJqG4c/UozKhRcEtSKOyW4txhxsUFb2PdU81TdI2if0yXrXqlyVrG+qeJ9dXvEwVPneukiU+mnM7dT68n/uXVc2rtNAqps5xQi8GiVq4YGdZrhjWlRUGq4wkXVvq/MnHOLRfk+yv5EqKfJ/8mxxuVaKuyeeDbYDDABCzBP1iDCLZhF/ahCjUQcAv38AhPwV3wEDwHL4PoUPA1swj/IXj9BCjknpQ=</latexit> hPropose, wi <latexit sha1_base64="h2O3ozeSV/xtPoxwVIvutDjG2ik=">AAAB7nicbVDLSgMxFL3js9ZX1aWbYBFclZmCj2XBjcuK9gHtUDJppg3NJENyRyilH+HGhSJu/R53/o1pOwttPRA4nHPvzb0nSqWw6Pvf3tr6xubWdmGnuLu3f3BYOjpuWp0ZxhtMS23aEbVcCsUbKFDydmo4TSLJW9Hodua3nrixQqtHHKc8TOhAiVgwik5qPaA2dMB7pbJf8ecgqyTISRly1Hulr25fsyzhCpmk1nYCP8VwQg0KJvm02M0sTykbudkdRxVNuA0n83Wn5NwpfRJr455CMld/d0xoYu04iVxlQnFol72Z+J/XyTC+CSdCpRlyxRYfxZkkqMnsdtIXhjOUY0coM8LtStiQGsrQJVR0IQTLJ6+SZrUSXFUu76vlGsnjKMApnMEFBHANNbiDOjSAwQie4RXevNR78d69j0Xpmpf3nMAfeJ8/WcWPew==</latexit> Storage <latexit sha1_base64="T+Jk6h+XJKdfIGSOCoCjuKSHLaA=">AAAB63icbVDJSgNBEK1xjXGLevTSGARPYSbgcgx48SQRzALJEHp6epImvQzdPUII+QUvHhTx6g9582/sSeagiQ8KHu9VUVUvSjkz1ve/vbX1jc2t7dJOeXdv/+CwcnTcNirThLaI4kp3I2woZ5K2LLOcdlNNsYg47UTj29zvPFFtmJKPdpLSUOChZAkj2ObSvYrpoFL1a/4caJUEBalCgeag8tWPFckElZZwbEwv8FMbTrG2jHA6K/czQ1NMxnhIe45KLKgJp/NbZ+jcKTFKlHYlLZqrvyemWBgzEZHrFNiOzLKXi/95vcwmN+GUyTSzVJLFoiTjyCqUP45ipimxfOIIJpq5WxEZYY2JdfGUXQjB8surpF2vBVe1y4d6tYGKOEpwCmdwAQFcQwPuoAktIDCCZ3iFN094L96797FoXfOKmRP4A+/zB+jTjg4=</latexit> Node <latexit sha1_base64="h2O3ozeSV/xtPoxwVIvutDjG2ik=">AAAB7nicbVDLSgMxFL3js9ZX1aWbYBFclZmCj2XBjcuK9gHtUDJppg3NJENyRyilH+HGhSJu/R53/o1pOwttPRA4nHPvzb0nSqWw6Pvf3tr6xubWdmGnuLu3f3BYOjpuWp0ZxhtMS23aEbVcCsUbKFDydmo4TSLJW9Hodua3nrixQqtHHKc8TOhAiVgwik5qPaA2dMB7pbJf8ecgqyTISRly1Hulr25fsyzhCpmk1nYCP8VwQg0KJvm02M0sTykbudkdRxVNuA0n83Wn5NwpfRJr455CMld/d0xoYu04iVxlQnFol72Z+J/XyTC+CSdCpRlyxRYfxZkkqMnsdtIXhjOUY0coM8LtStiQGsrQJVR0IQTLJ6+SZrUSXFUu76vlGsnjKMApnMEFBHANNbiDOjSAwQie4RXevNR78d69j0Xpmpf3nMAfeJ8/WcWPew==</latexit> Storage <latexit sha1_base64="T+Jk6h+XJKdfIGSOCoCjuKSHLaA=">AAAB63icbVDJSgNBEK1xjXGLevTSGARPYSbgcgx48SQRzALJEHp6epImvQzdPUII+QUvHhTx6g9582/sSeagiQ8KHu9VUVUvSjkz1ve/vbX1jc2t7dJOeXdv/+CwcnTcNirThLaI4kp3I2woZ5K2LLOcdlNNsYg47UTj29zvPFFtmJKPdpLSUOChZAkj2ObSvYrpoFL1a/4caJUEBalCgeag8tWPFckElZZwbEwv8FMbTrG2jHA6K/czQ1NMxnhIe45KLKgJp/NbZ+jcKTFKlHYlLZqrvyemWBgzEZHrFNiOzLKXi/95vcwmN+GUyTSzVJLFoiTjyCqUP45ipimxfOIIJpq5WxEZYY2JdfGUXQjB8surpF2vBVe1y4d6tYGKOEpwCmdwAQFcQwPuoAktIDCCZ3iFN094L96797FoXfOKmRP4A+/zB+jTjg4=</latexit> Node <latexit sha1_base64="lglUUIPFiryJvS6ajhKy1JEJAwQ=">AAAB73icbVDJSgNBEK2JW4xb1KOXxiDES5gJuBwDXjx4iGAWSIbQ01OTNOlZ7O4RwpCf8OJBEa/+jjf/xk4yB018UPB4r4qqel4iuNK2/W0V1tY3NreK26Wd3b39g/LhUVvFqWTYYrGIZdejCgWPsKW5FthNJNLQE9jxxjczv/OEUvE4etCTBN2QDiMecEa1kbrVO6Q+yvNBuWLX7DnIKnFyUoEczUH5q+/HLA0x0kxQpXqOnWg3o1JzJnBa6qcKE8rGdIg9QyMaonKz+b1TcmYUnwSxNBVpMld/T2Q0VGoSeqYzpHqklr2Z+J/XS3Vw7WY8SlKNEVssClJBdExmzxOfS2RaTAyhTHJzK2EjKinTJqKSCcFZfnmVtOs157J2cV+vNEgeRxFO4BSq4MAVNOAWmtACBgKe4RXerEfrxXq3PhatBSufOYY/sD5/ACutj04=</latexit> (Leader) <latexit sha1_base64="h2O3ozeSV/xtPoxwVIvutDjG2ik=">AAAB7nicbVDLSgMxFL3js9ZX1aWbYBFclZmCj2XBjcuK9gHtUDJppg3NJENyRyilH+HGhSJu/R53/o1pOwttPRA4nHPvzb0nSqWw6Pvf3tr6xubWdmGnuLu3f3BYOjpuWp0ZxhtMS23aEbVcCsUbKFDydmo4TSLJW9Hodua3nrixQqtHHKc8TOhAiVgwik5qPaA2dMB7pbJf8ecgqyTISRly1Hulr25fsyzhCpmk1nYCP8VwQg0KJvm02M0sTykbudkdRxVNuA0n83Wn5NwpfRJr455CMld/d0xoYu04iVxlQnFol72Z+J/XyTC+CSdCpRlyxRYfxZkkqMnsdtIXhjOUY0coM8LtStiQGsrQJVR0IQTLJ6+SZrUSXFUu76vlGsnjKMApnMEFBHANNbiDOjSAwQie4RXevNR78d69j0Xpmpf3nMAfeJ8/WcWPew==</latexit> Storage <latexit sha1_base64="T+Jk6h+XJKdfIGSOCoCjuKSHLaA=">AAAB63icbVDJSgNBEK1xjXGLevTSGARPYSbgcgx48SQRzALJEHp6epImvQzdPUII+QUvHhTx6g9582/sSeagiQ8KHu9VUVUvSjkz1ve/vbX1jc2t7dJOeXdv/+CwcnTcNirThLaI4kp3I2woZ5K2LLOcdlNNsYg47UTj29zvPFFtmJKPdpLSUOChZAkj2ObSvYrpoFL1a/4caJUEBalCgeag8tWPFckElZZwbEwv8FMbTrG2jHA6K/czQ1NMxnhIe45KLKgJp/NbZ+jcKTFKlHYlLZqrvyemWBgzEZHrFNiOzLKXi/95vcwmN+GUyTSzVJLFoiTjyCqUP45ipimxfOIIJpq5WxEZYY2JdfGUXQjB8surpF2vBVe1y4d6tYGKOEpwCmdwAQFcQwPuoAktIDCCZ3iFN094L96797FoXfOKmRP4A+/zB+jTjg4=</latexit> Node <latexit sha1_base64="KRHsJUmjM4YZw6/kOFSlk749aEM=">AAACEHicbVA9SwNBEJ3z2/gVtRRkUUQLCXeCH6ViY5mIUSEXwt5mEhf39o7dOTEcKS1t/Cs2ForYWtr5G/wTbhILvx4MPN6bYWZelCppyfffvaHhkdGx8YnJwtT0zOxccX7h1CaZEVgViUrMecQtKqmxSpIUnqcGeRwpPIsuD3v+2RUaKxN9Qp0U6zFva9mSgpOTGsX1UHHdVshCwmuyIj8QAlPCZneT6U12xULT9xvFVb/k98H+kuCLrO5D5eNm+eG43Ci+hc1EZDFqEopbWwv8lOo5NySFwm4hzCymXFzyNtYc1TxGW8/7D3XZmlOarJUYV5pYX/0+kfPY2k4cuc6Y04X97fXE/7xaRq29ei51mhFqMVjUyhSjhPXSYU1pUJDqOMKFke5WJi644YJchgUXQvD75b/kdKsU7JS2Ky4NBgNMwBKswAYEsAv7cARlqIKAW7iHR3jy7rwH79l7GbQOeV8zi/AD3usnUZSfpg==</latexit> hAccepted, n, vi <latexit sha1_base64="0bbFrU8XFIfEIJGZQJHOrtrxm3g=">AAACEHicbVA9SwNBEJ3z2/gVtRRkUUQLCXeCH2XExlLFqJALYW8ziYt7e8funBqOlJY2/hUbC0VsLe38Df4JN4mFXw8GHu/NMDMvSpW05Pvv3sDg0PDI6Nh4YWJyanqmODt3YpPMCKyIRCXmLOIWldRYIUkKz1KDPI4UnkYXe13/9BKNlYk+pnaKtZi3tGxKwclJ9eJqqLhuKWQh4TVZke8KgSlho7PO4nV2xULT8+vFZb/k98D+kuCLLJfh8ONm8eHooF58CxuJyGLUJBS3thr4KdVybkgKhZ1CmFlMubjgLaw6qnmMtpb3HuqwFac0WDMxrjSxnvp9Iuexte04cp0xp3P72+uK/3nVjJo7tVzqNCPUor+omSlGCeumwxrSoCDVdoQLI92tTJxzwwW5DAsuhOD3y3/JyUYp2CptHro0GPQxBguwBGsQwDaUYR8OoAICbuEeHuHJu/MevGfvpd864H3NzMMPeK+fUZGfpg==</latexit> hAccepted, m, wi <latexit sha1_base64="lglUUIPFiryJvS6ajhKy1JEJAwQ=">AAAB73icbVDJSgNBEK2JW4xb1KOXxiDES5gJuBwDXjx4iGAWSIbQ01OTNOlZ7O4RwpCf8OJBEa/+jjf/xk4yB018UPB4r4qqel4iuNK2/W0V1tY3NreK26Wd3b39g/LhUVvFqWTYYrGIZdejCgWPsKW5FthNJNLQE9jxxjczv/OEUvE4etCTBN2QDiMecEa1kbrVO6Q+yvNBuWLX7DnIKnFyUoEczUH5q+/HLA0x0kxQpXqOnWg3o1JzJnBa6qcKE8rGdIg9QyMaonKz+b1TcmYUnwSxNBVpMld/T2Q0VGoSeqYzpHqklr2Z+J/XS3Vw7WY8SlKNEVssClJBdExmzxOfS2RaTAyhTHJzK2EjKinTJqKSCcFZfnmVtOs157J2cV+vNEgeRxFO4BSq4MAVNOAWmtACBgKe4RXerEfrxXq3PhatBSufOYY/sD5/ACutj04=</latexit> (Leader) <latexit sha1_base64="h2O3ozeSV/xtPoxwVIvutDjG2ik=">AAAB7nicbVDLSgMxFL3js9ZX1aWbYBFclZmCj2XBjcuK9gHtUDJppg3NJENyRyilH+HGhSJu/R53/o1pOwttPRA4nHPvzb0nSqWw6Pvf3tr6xubWdmGnuLu3f3BYOjpuWp0ZxhtMS23aEbVcCsUbKFDydmo4TSLJW9Hodua3nrixQqtHHKc8TOhAiVgwik5qPaA2dMB7pbJf8ecgqyTISRly1Hulr25fsyzhCpmk1nYCP8VwQg0KJvm02M0sTykbudkdRxVNuA0n83Wn5NwpfRJr455CMld/d0xoYu04iVxlQnFol72Z+J/XyTC+CSdCpRlyxRYfxZkkqMnsdtIXhjOUY0coM8LtStiQGsrQJVR0IQTLJ6+SZrUSXFUu76vlGsnjKMApnMEFBHANNbiDOjSAwQie4RXevNR78d69j0Xpmpf3nMAfeJ8/WcWPew==</latexit> Storage <latexit sha1_base64="T+Jk6h+XJKdfIGSOCoCjuKSHLaA=">AAAB63icbVDJSgNBEK1xjXGLevTSGARPYSbgcgx48SQRzALJEHp6epImvQzdPUII+QUvHhTx6g9582/sSeagiQ8KHu9VUVUvSjkz1ve/vbX1jc2t7dJOeXdv/+CwcnTcNirThLaI4kp3I2woZ5K2LLOcdlNNsYg47UTj29zvPFFtmJKPdpLSUOChZAkj2ObSvYrpoFL1a/4caJUEBalCgeag8tWPFckElZZwbEwv8FMbTrG2jHA6K/czQ1NMxnhIe45KLKgJp/NbZ+jcKTFKlHYlLZqrvyemWBgzEZHrFNiOzLKXi/95vcwmN+GUyTSzVJLFoiTjyCqUP45ipimxfOIIJpq5WxEZYY2JdfGUXQjB8surpF2vBVe1y4d6tYGKOEpwCmdwAQFcQwPuoAktIDCCZ3iFN094L96797FoXfOKmRP4A+/zB+jTjg4=</latexit> Node <latexit sha1_base64="h2O3ozeSV/xtPoxwVIvutDjG2ik=">AAAB7nicbVDLSgMxFL3js9ZX1aWbYBFclZmCj2XBjcuK9gHtUDJppg3NJENyRyilH+HGhSJu/R53/o1pOwttPRA4nHPvzb0nSqWw6Pvf3tr6xubWdmGnuLu3f3BYOjpuWp0ZxhtMS23aEbVcCsUbKFDydmo4TSLJW9Hodua3nrixQqtHHKc8TOhAiVgwik5qPaA2dMB7pbJf8ecgqyTISRly1Hulr25fsyzhCpmk1nYCP8VwQg0KJvm02M0sTykbudkdRxVNuA0n83Wn5NwpfRJr455CMld/d0xoYu04iVxlQnFol72Z+J/XyTC+CSdCpRlyxRYfxZkkqMnsdtIXhjOUY0coM8LtStiQGsrQJVR0IQTLJ6+SZrUSXFUu76vlGsnjKMApnMEFBHANNbiDOjSAwQie4RXevNR78d69j0Xpmpf3nMAfeJ8/WcWPew==</latexit> Storage <latexit sha1_base64="T+Jk6h+XJKdfIGSOCoCjuKSHLaA=">AAAB63icbVDJSgNBEK1xjXGLevTSGARPYSbgcgx48SQRzALJEHp6epImvQzdPUII+QUvHhTx6g9582/sSeagiQ8KHu9VUVUvSjkz1ve/vbX1jc2t7dJOeXdv/+CwcnTcNirThLaI4kp3I2woZ5K2LLOcdlNNsYg47UTj29zvPFFtmJKPdpLSUOChZAkj2ObSvYrpoFL1a/4caJUEBalCgeag8tWPFckElZZwbEwv8FMbTrG2jHA6K/czQ1NMxnhIe45KLKgJp/NbZ+jcKTFKlHYlLZqrvyemWBgzEZHrFNiOzLKXi/95vcwmN+GUyTSzVJLFoiTjyCqUP45ipimxfOIIJpq5WxEZYY2JdfGUXQjB8surpF2vBVe1y4d6tYGKOEpwCmdwAQFcQwPuoAktIDCCZ3iFN094L96797FoXfOKmRP4A+/zB+jTjg4=</latexit> Node <latexit sha1_base64="h2O3ozeSV/xtPoxwVIvutDjG2ik=">AAAB7nicbVDLSgMxFL3js9ZX1aWbYBFclZmCj2XBjcuK9gHtUDJppg3NJENyRyilH+HGhSJu/R53/o1pOwttPRA4nHPvzb0nSqWw6Pvf3tr6xubWdmGnuLu3f3BYOjpuWp0ZxhtMS23aEbVcCsUbKFDydmo4TSLJW9Hodua3nrixQqtHHKc8TOhAiVgwik5qPaA2dMB7pbJf8ecgqyTISRly1Hulr25fsyzhCpmk1nYCP8VwQg0KJvm02M0sTykbudkdRxVNuA0n83Wn5NwpfRJr455CMld/d0xoYu04iVxlQnFol72Z+J/XyTC+CSdCpRlyxRYfxZkkqMnsdtIXhjOUY0coM8LtStiQGsrQJVR0IQTLJ6+SZrUSXFUu76vlGsnjKMApnMEFBHANNbiDOjSAwQie4RXevNR78d69j0Xpmpf3nMAfeJ8/WcWPew==</latexit> Storage <latexit sha1_base64="T+Jk6h+XJKdfIGSOCoCjuKSHLaA=">AAAB63icbVDJSgNBEK1xjXGLevTSGARPYSbgcgx48SQRzALJEHp6epImvQzdPUII+QUvHhTx6g9582/sSeagiQ8KHu9VUVUvSjkz1ve/vbX1jc2t7dJOeXdv/+CwcnTcNirThLaI4kp3I2woZ5K2LLOcdlNNsYg47UTj29zvPFFtmJKPdpLSUOChZAkj2ObSvYrpoFL1a/4caJUEBalCgeag8tWPFckElZZwbEwv8FMbTrG2jHA6K/czQ1NMxnhIe45KLKgJp/NbZ+jcKTFKlHYlLZqrvyemWBgzEZHrFNiOzLKXi/95vcwmN+GUyTSzVJLFoiTjyCqUP45ipimxfOIIJpq5WxEZYY2JdfGUXQjB8surpF2vBVe1y4d6tYGKOEpwCmdwAQFcQwPuoAktIDCCZ3iFN094L96797FoXfOKmRP4A+/zB+jTjg4=</latexit> Node <latexit 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sha1_base64="uazShLoOvpBY8op2KmaCNIJcD70=">AAACC3icbVDJSgNBEO1xjXGLevTSJAgeJMyI2zHixWMEs0AmhJ5OJWnS0zN016hhyN2Lv+LFgyJe/QFv/o2d5aCJDwoe71VRVS+IpTDout/OwuLS8spqZi27vrG5tZ3b2a2aKNEcKjySka4HzIAUCiooUEI91sDCQEIt6F+N/NodaCMidYuDGJoh6yrREZyhlVq5vC+Z6kqgPsIDGp5ecg4xDo/oPfX12GrlCm7RHYPOE29KCmSKciv35bcjnoSgkEtmTMNzY2ymTKPgEoZZPzEQM95nXWhYqlgIppmOfxnSA6u0aSfSthTSsfp7ImWhMYMwsJ0hw56Z9Ubif14jwc5FMxUqThAUnyzqJJJiREfB0LbQwFEOLGFcC3sr5T2mGUcbX9aG4M2+PE+qx0XvrHh6c1Io0WkcGbJP8uSQeOSclMg1KZMK4eSRPJNX8uY8OS/Ou/MxaV1wpjN75A+czx/OQJrN</latexit> hAccept, wi <latexit sha1_base64="EZokVHlYXKH7zgUPxYYvTr21hFc=">AAAB8XicbVBNTwIxEJ3FL8Qv1KOXRjDxRHZJ/DiSePGIRsAIG9LtdqGh227arpFs+BdePGiMV/+NN/+NBfag4EsmeXlvJjPzgoQzbVz32ymsrK6tbxQ3S1vbO7t75f2DtpapIrRFJJfqPsCaciZoyzDD6X2iKI4DTjvB6Grqdx6p0kyKOzNOqB/jgWARI9hY6eGWEqlCVH2q9ssVt+bOgJaJl5MK5Gj2y1+9UJI0psIQjrXuem5i/Awrwwink1Iv1TTBZIQHtGupwDHVfja7eIJOrBKiSCpbwqCZ+nsiw7HW4ziwnTE2Q73oTcX/vG5qoks/YyJJDRVkvihKOTISTd9HIVOUGD62BBPF7K2IDLHCxNiQSjYEb/HlZdKu17zz2tlNvdJAeRxFOIJjOAUPLqAB19CEFhAQ8Ayv8OZo58V5dz7mrQUnnzmEP3A+fwBxJJAD</latexit> Record x <latexit 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15. クォーラムにおけるドメイン制約 (1) <latexit sha1_base64="zPwICzsTAmFT/FKLOANf8a/3n78=">AAACBXicbVDJSgNBEO2JW4xb1KMeGoPgKcyI2zHgxZNENAtkQujpVJImPdNDd40Yhly8+CtePCji1X/w5t/YWQ6a+KDg8V4VVfWCWAqDrvvtZBYWl5ZXsqu5tfWNza389k7VqERzqHAlla4HzIAUEVRQoIR6rIGFgYRa0L8c+bV70Eao6A4HMTRD1o1ER3CGVmrl932EB0xvUWnWhaHv5ybCtWrDsJUvuEV3DDpPvCkpkCnKrfyX31Y8CSFCLpkxDc+NsZkyjYJLGOb8xEDMeN+ualgasRBMMx1/MaSHVmnTjtK2IqRj9fdEykJjBmFgO0OGPTPrjcT/vEaCnYtmKqI4QYj4ZFEnkRQVHUVC20IDRzmwhHEt7K2U95hmHG1wORuCN/vyPKkeF72z4unNSaFEp3FkyR45IEfEI+ekRK5ImVQIJ4/kmbySN+fJeXHenY9Ja8aZzuySP3A+fwBIJ5j6</latexit> Storage Node <latexit 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sha1_base64="zPwICzsTAmFT/FKLOANf8a/3n78=">AAACBXicbVDJSgNBEO2JW4xb1KMeGoPgKcyI2zHgxZNENAtkQujpVJImPdNDd40Yhly8+CtePCji1X/w5t/YWQ6a+KDg8V4VVfWCWAqDrvvtZBYWl5ZXsqu5tfWNza389k7VqERzqHAlla4HzIAUEVRQoIR6rIGFgYRa0L8c+bV70Eao6A4HMTRD1o1ER3CGVmrl932EB0xvUWnWhaHv5ybCtWrDsJUvuEV3DDpPvCkpkCnKrfyX31Y8CSFCLpkxDc+NsZkyjYJLGOb8xEDMeN+ualgasRBMMx1/MaSHVmnTjtK2IqRj9fdEykJjBmFgO0OGPTPrjcT/vEaCnYtmKqI4QYj4ZFEnkRQVHUVC20IDRzmwhHEt7K2U95hmHG1wORuCN/vyPKkeF72z4unNSaFEp3FkyR45IEfEI+ekRK5ImVQIJ4/kmbySN+fJeXHenY9Ja8aZzuySP3A+fwBIJ5j6</latexit> Storage Node <latexit sha1_base64="zPwICzsTAmFT/FKLOANf8a/3n78=">AAACBXicbVDJSgNBEO2JW4xb1KMeGoPgKcyI2zHgxZNENAtkQujpVJImPdNDd40Yhly8+CtePCji1X/w5t/YWQ6a+KDg8V4VVfWCWAqDrvvtZBYWl5ZXsqu5tfWNza389k7VqERzqHAlla4HzIAUEVRQoIR6rIGFgYRa0L8c+bV70Eao6A4HMTRD1o1ER3CGVmrl932EB0xvUWnWhaHv5ybCtWrDsJUvuEV3DDpPvCkpkCnKrfyX31Y8CSFCLpkxDc+NsZkyjYJLGOb8xEDMeN+ualgasRBMMx1/MaSHVmnTjtK2IqRj9fdEykJjBmFgO0OGPTPrjcT/vEaCnYtmKqI4QYj4ZFEnkRQVHUVC20IDRzmwhHEt7K2U95hmHG1wORuCN/vyPKkeF72z4unNSaFEp3FkyR45IEfEI+ekRK5ImVQIJ4/kmbySN+fJeXHenY9Ja8aZzuySP3A+fwBIJ5j6</latexit> Storage Node <latexit sha1_base64="lqq6nFD7tTE3DbBDHupk9EmW+cQ=">AAAB63icbVBNSwMxEJ2tX7V+VT16CbaCF8tuoeqx4MVjBfsB7VKyabYNTbJLkhXK0r/gxYMiXv1D3vw3Zts9aOuDgcd7M8zMC2LOtHHdb6ewsbm1vVPcLe3tHxwelY9POjpKFKFtEvFI9QKsKWeStg0znPZiRbEIOO0G07vM7z5RpVkkH80spr7AY8lCRrDJpOqVVx2WK27NXQCtEy8nFcjRGpa/BqOIJIJKQzjWuu+5sfFTrAwjnM5Lg0TTGJMpHtO+pRILqv10cescXVhlhMJI2ZIGLdTfEykWWs9EYDsFNhO96mXif14/MeGtnzIZJ4ZKslwUJhyZCGWPoxFTlBg+swQTxeytiEywwsTYeEo2BG/15XXSqde861rjoV5pojyOIpzBOVyCBzfQhHtoQRsITOAZXuHNEc6L8+58LFsLTj5zCn/gfP4AlA+NLg==</latexit> 1 <latexit 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sha1_base64="lqq6nFD7tTE3DbBDHupk9EmW+cQ=">AAAB63icbVBNSwMxEJ2tX7V+VT16CbaCF8tuoeqx4MVjBfsB7VKyabYNTbJLkhXK0r/gxYMiXv1D3vw3Zts9aOuDgcd7M8zMC2LOtHHdb6ewsbm1vVPcLe3tHxwelY9POjpKFKFtEvFI9QKsKWeStg0znPZiRbEIOO0G07vM7z5RpVkkH80spr7AY8lCRrDJpOqVVx2WK27NXQCtEy8nFcjRGpa/BqOIJIJKQzjWuu+5sfFTrAwjnM5Lg0TTGJMpHtO+pRILqv10cescXVhlhMJI2ZIGLdTfEykWWs9EYDsFNhO96mXif14/MeGtnzIZJ4ZKslwUJhyZCGWPoxFTlBg+swQTxeytiEywwsTYeEo2BG/15XXSqde861rjoV5pojyOIpzBOVyCBzfQhHtoQRsITOAZXuHNEc6L8+58LFsLTj5zCn/gfP4AlA+NLg==</latexit> 1 <latexit sha1_base64="lqq6nFD7tTE3DbBDHupk9EmW+cQ=">AAAB63icbVBNSwMxEJ2tX7V+VT16CbaCF8tuoeqx4MVjBfsB7VKyabYNTbJLkhXK0r/gxYMiXv1D3vw3Zts9aOuDgcd7M8zMC2LOtHHdb6ewsbm1vVPcLe3tHxwelY9POjpKFKFtEvFI9QKsKWeStg0znPZiRbEIOO0G07vM7z5RpVkkH80spr7AY8lCRrDJpOqVVx2WK27NXQCtEy8nFcjRGpa/BqOIJIJKQzjWuu+5sfFTrAwjnM5Lg0TTGJMpHtO+pRILqv10cescXVhlhMJI2ZIGLdTfEykWWs9EYDsFNhO96mXif14/MeGtnzIZJ4ZKslwUJhyZCGWPoxFTlBg+swQTxeytiEywwsTYeEo2BG/15XXSqde861rjoV5pojyOIpzBOVyCBzfQhHtoQRsITOAZXuHNEc6L8+58LFsLTj5zCn/gfP4AlA+NLg==</latexit> 1 <latexit 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sha1_base64="zPwICzsTAmFT/FKLOANf8a/3n78=">AAACBXicbVDJSgNBEO2JW4xb1KMeGoPgKcyI2zHgxZNENAtkQujpVJImPdNDd40Yhly8+CtePCji1X/w5t/YWQ6a+KDg8V4VVfWCWAqDrvvtZBYWl5ZXsqu5tfWNza389k7VqERzqHAlla4HzIAUEVRQoIR6rIGFgYRa0L8c+bV70Eao6A4HMTRD1o1ER3CGVmrl932EB0xvUWnWhaHv5ybCtWrDsJUvuEV3DDpPvCkpkCnKrfyX31Y8CSFCLpkxDc+NsZkyjYJLGOb8xEDMeN+ualgasRBMMx1/MaSHVmnTjtK2IqRj9fdEykJjBmFgO0OGPTPrjcT/vEaCnYtmKqI4QYj4ZFEnkRQVHUVC20IDRzmwhHEt7K2U95hmHG1wORuCN/vyPKkeF72z4unNSaFEp3FkyR45IEfEI+ekRK5ImVQIJ4/kmbySN+fJeXHenY9Ja8aZzuySP3A+fwBIJ5j6</latexit> Storage Node <latexit 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sha1_base64="zPwICzsTAmFT/FKLOANf8a/3n78=">AAACBXicbVDJSgNBEO2JW4xb1KMeGoPgKcyI2zHgxZNENAtkQujpVJImPdNDd40Yhly8+CtePCji1X/w5t/YWQ6a+KDg8V4VVfWCWAqDrvvtZBYWl5ZXsqu5tfWNza389k7VqERzqHAlla4HzIAUEVRQoIR6rIGFgYRa0L8c+bV70Eao6A4HMTRD1o1ER3CGVmrl932EB0xvUWnWhaHv5ybCtWrDsJUvuEV3DDpPvCkpkCnKrfyX31Y8CSFCLpkxDc+NsZkyjYJLGOb8xEDMeN+ualgasRBMMx1/MaSHVmnTjtK2IqRj9fdEykJjBmFgO0OGPTPrjcT/vEaCnYtmKqI4QYj4ZFEnkRQVHUVC20IDRzmwhHEt7K2U95hmHG1wORuCN/vyPKkeF72z4unNSaFEp3FkyR45IEfEI+ekRK5ImVQIJ4/kmbySN+fJeXHenY9Ja8aZzuySP3A+fwBIJ5j6</latexit> Storage Node <latexit 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sha1_base64="JOzmiYlisLzJ8RsvYXEJfIMvYJ0=">AAAB+3icbVDLSgMxFL1TX7W+xrp0E2wFV2Wm+NoIRTcuK9gHtEPJpJk2NJMZkkyxDP0VNy4UceuPuPNvTNtZaOuBwOGce7g3x485U9pxvq3c2vrG5lZ+u7Czu7d/YB8WmypKJKENEvFItn2sKGeCNjTTnLZjSXHoc9ryR3czvzWmUrFIPOpJTL0QDwQLGMHaSD27eGvCaIx5QlG5jW7Qeblnl5yKMwdaJW5GSpCh3rO/uv2IJCEVmnCsVMd1Yu2lWGpGOJ0WuomiMSYjPKAdQwUOqfLS+e1TdGqUPgoiaZ7QaK7+TqQ4VGoS+mYyxHqolr2Z+J/XSXRw7aVMxImmgiwWBQlHOkKzIlCfSUo0nxiCiWTmVkSGWGKiTV0FU4K7/OVV0qxW3MvKxUO1VENZHXk4hhM4AxeuoAb3UIcGEHiCZ3iFN2tqvVjv1sdiNGdlmSP4A+vzBxpukm4=</latexit> Base value X = 4 <latexit sha1_base64="hbSVeECI30iKw3XstcQ0pKdwmtI=">AAACDHicbVDLSgMxFM34rPVVdekmWAQ3DjPioxuh4MaFlAr2AZ2hZDKZNjSTjElGKMN8gBt/xY0LRdz6Ae78G9PHQlsPBA7nnMvNPUHCqNKO820tLC4tr6wW1orrG5tb26Wd3aYSqcSkgQUTsh0gRRjlpKGpZqSdSILigJFWMLga+a0HIhUV/E4PE+LHqMdpRDHSRuqWyjfwEnqRRDirwWN4343yrJZDD4dCw7bxHLtiUo7tjAHniTslZTBFvVv68kKB05hwjRlSquM6ifYzJDXFjORFL1UkQXiAeqRjKEcxUX42PiaHh0YJYSSkeVzDsfp7IkOxUsM4MMkY6b6a9Ubif14n1VHFzyhPUk04niyKUga1gKNmYEglwZoNDUFYUvNXiPvINKNNf0VTgjt78jxpntjuuX12e1quwmkdBbAPDsARcMEFqIJrUAcNgMEjeAav4M16sl6sd+tjEl2wpjN74A+szx9mfJiS</latexit> L = N qf N · X = 0.8 <latexit sha1_base64="oy2A8CSFP2EjSzR7NjJ1/VJ7yEI=">AAAB+3icbVDLSgNBEJyNrxhfMR69DAYhXsJuwMcx4MWTRDAPSJbQOzubDJmZXWZmxRDyK148KOLVH/Hm3zhJVtDEgoaiqpvuriDhTBvX/XJya+sbm1v57cLO7t7+QfGw1NJxqghtkpjHqhOAppxJ2jTMcNpJFAURcNoORtczv/1AlWaxvDfjhPoCBpJFjICxUr9YqsAZvo1xSAWoH7HsVt058CrxMlJGGRr94mcvjEkqqDSEg9Zdz02MPwFlGOF0WuilmiZARjCgXUslCKr9yfz2KT61SoijWNmSBs/V3xMTEFqPRWA7BZihXvZm4n9eNzXRlT9hMkkNlWSxKEo5NjGeBYFDpigxfGwJEMXsrZgMQQExNq6CDcFbfnmVtGpV76J6flcr13EWRx4doxNUQR66RHV0gxqoiQh6RE/oBb06U+fZeXPeF605J5s5Qn/gfHwDrTqTew==</latexit> (a) No demarcation <latexit sha1_base64="YNtTVoW2+iMNKdac2XppVJTsN+w=">AAAB+HicbVDLSgNBEOyNrxgfiXr0MhiEeAm7AR/HgB48RjAPSJYwO5lNhszMLjOzQlzyJV48KOLVT/Hm3zhJVtDEgoaiqpvuriDmTBvX/XJya+sbm1v57cLO7t5+sXRw2NJRoghtkohHqhNgTTmTtGmY4bQTK4pFwGk7GF/P/PYDVZpF8t5MYuoLPJQsZAQbK/VLxUpwhm6owOpHKbtVdw60SryMlCFDo1/67A0ikggqDeFY667nxsZPsTKMcDot9BJNY0zGeEi7lkosqPbT+eFTdGqVAQojZUsaNFd/T6RYaD0Rge0U2Iz0sjcT//O6iQmv/JTJODFUksWiMOHIRGiWAhowRYnhE0swUczeisgIK0yMzapgQ/CWX14lrVrVu6ie39XKdZTFkYdjOIEKeHAJdbiFBjSBQAJP8AKvzqPz7Lw574vWnJPNHMEfOB/fsZaSYQ==</latexit> (b) Demarcation 11
16. クォーラムにおけるドメイン制約 (2) • 非負制約を与えた属性とその属性値をデクリメントするトランザクションを考える．属性 のベース値を X，m をコミットしたトランザクション数，δi をトランザクション i のデク リメント値とすると，以下を満たすとき，X は 0 に更新されることが期待される． m ∑ i=1 δi = X. • MDCC において，複数のデクリメントが同時にコミットされるのは，それらのオプション がサイズ qf の高速クォーラムで受理されたときである．したがって，m 個のトランザクシ ョンがコミットされた場合でも X が (N − qf ) · X に更新されている可能性がある． • デクリメントした値が以下のしきい値を下回らない場合にのみオプションを受理するよう にすることで，この問題を回避することができる． L = N − qf N · X. 12
17. Evaluation
18. セットアップ • 5 つの DC (California, Virginia, Ireland, Singapore, Tokyo) にレプリケーションする． • 各 DC は完全なレプリカを持つ． • 各テーブルは DC 内の 4 台のストレージノードにレンジパーティション化されている． • MDCC (read committed) と比較するプロトコルは以下のとおり． • Quorum Writes (QW-{3, 4}): 任意の書き込みリクエストに対してクォーラム (サイズ: 3, 4) からのレスポンスを待つもの．読み取りには単一のローカルレプリカを利用． • Two-phase Commit (2PC): トランザクションに関与するすべてのストレージノードで Prepare が成功した後に Commit するもの． • Megastore*: Megastore [7] を追実装したもの．シャーディングしない (i.e., 2PC を利用 しない)，read committed を利用する，Paxos-CP [4] の最適化を適用するなどの変更を 追加．すべてのマスターとクライアントを単一の DC に配置． 13
19. TPC-W: 書き込みトランザクションの遅延 スケールファクター 10K，地理的に均等に配置された 100 台のクライアントを用いて実験． • MDCC のコミット遅延は 2PC のおよそ半分． MDCC はほとんどのトランザクションを 1 RTT でコ ミット可能な一方で，2PC は 2 RTT を要する． • MDCC はより強い一貫性を保証しながら QW-4 と同 等のコミット遅延を実現． MDCC は高速クォーラムに QW-4 と同じサイズのク ォーラムを用いる． • Megastore* はすべてのトランザクションを Paxos で 直列化する必要があり，キュー待ちが発生． 0 10 20 30 40 50 60 70 80 90 100 100 200 400 1000 2000 4000 10000 20000 40000 Percentage of Transactions Write Transaction Response Times, log-scale (ms) QW-3 QW-4 MDCC 2PC Megastore* 0 200 400 600 800 1000 1200 1400 1600 Transactions per Second Figure 3. TPC-W write transaction re- sponse times CDF Fig on and finally Megastore* with slowest times. T sponse times are: 188ms for QW-3, 260ms for for MDCC, 668ms for 2PC, and 17,810ms for Since MDCC uses fast ballots whenever po 14
20. TPC-W: スケーラビリティ (クライアント数, スケールファクター) を (50, 5K), (100, 10K), (200, 20K) と変化させ，1 台あたり のテーブルサイズが 2.5K となるようにノードを追加して実験． • MDCC は QW と同等のスループットを達成． 2PC は 2 ラウンド目の待ちによりスループットが大 きく低下した． Megastore* はすべてのトランザクションが単一シャ ードで直列化されるため，スループットが出ない． • MDCC は QW や 2PC と同様に高スケーラビリティ． 0 10 20 30 40 50 60 70 80 90 100 100 200 400 1000 2000 4000 10000 20000 40000 Percentage of Transactions Write Transaction Response Times, log-scale (ms) QW-3 QW-4 MDCC 2PC Megastore* 0 200 400 600 800 1000 1200 1400 1600 50 100 200 Transactions per Second # Concurrent Clients QW-3 QW-4 MDCC 2PC Megastore* 0 10 20 30 40 50 60 70 80 90 100 0 Percentage of Transactions Figure 3. TPC-W write transaction re- sponse times CDF Figure 4. TPC-W transactions per sec- ond scalability Fig tim and finally Megastore* with slowest times. The median re- sponse times are: 188ms for QW-3, 260ms for QW-4, 278ms for MDCC, 668ms for 2PC, and 17,810ms for Megastore*. Since MDCC uses fast ballots whenever possible, MDCC (200 clients, 20,000 ite the amount of data per of 2,500 items and sca (keeping the ratio of c 15
21. マイクロベンチ: 最適化の効果 商品の在庫を管理する単一のテーブルに対して，3 つの商品を選んでそれぞれの在庫を 1–3 だ け減らすトランザクションを実行し，MDCC の各種最適化の効果を調査． • 2PC: 2 RTT 必要かつ，すべての DC からレスポンスを 待つ必要があるため遅い． • MDCC (Multi): 各行の書き込みリクエストを 4/5 の確 率でリモートのリーダーに転送するため 2 RTT が必 要だが，過半数の DC からレスポンスを待てばよい． • MDCC (Fast): ほとんどの場合でリーダーにアクセス する必要がなく，1 RTT でコミット可能なため速い． • MDCC (Full): 加えて，可換性の活用によりコンフリ クトと衝突が低減されるため速い． 200 400 1000 2000 4000 10000 20000 40000 Write Transaction Response Times, log-scale (ms) QW-3 QW-4 MDCC 2PC Megastore* 0 200 400 600 800 1000 1200 1400 1600 50 100 200 Transactions per Second # Concurrent Clients QW-3 QW-4 MDCC 2PC Megastore* 0 10 20 30 40 50 60 70 80 90 100 0 100 200 300 400 500 600 700 800 900 Percentage of Transactions Write Transaction Response Times (ms) MDCC Fast Multi 2PC e 3. TPC-W write transaction re- e times CDF Figure 4. TPC-W transactions per sec- ond scalability Figure 5. Micro-benchmark response times CDF ally Megastore* with slowest times. The median re- times are: 188ms for QW-3, 260ms for QW-4, 278ms CC, 668ms for 2PC, and 17,810ms for Megastore*. e MDCC uses fast ballots whenever possible, MDCC (200 clients, 20,000 items). For each configuration, we fixed the amount of data per storage node to a TPC-W scale-factor of 2,500 items and scaled the number of nodes accordingly (keeping the ratio of clients to storage nodes constant). For 16
22. マイクロベンチマーク: コンフリクトの影響 ホットスポットのサイズを小さくすることでコンフリクト率を増大させ，その影響を調査． • コンフリクト率が増大すると MDCC (Fast/Full) の性 能は大きく低下する． MDCC (Multi) は，リーダーを用いてトランザクショ ンを直列化するため，トランザクションのコンフリ クトが Paxos の衝突を引き起こさない． MDCC (Fast/Full) は，トランザクションのコンフリク トにより高速パスで衝突が発生し，通常パスがトリ ガーされる．衝突の解消には MDCC (Multi) よりも多 くのメッセージが必要である． • コンフリクト率が高い場合は，リーダーベースのア プローチの方が優れる． 0 10 20 30 40 50 60 70 80 2PC M ulti Fast M DCC 2PC M ulti Fast M DCC 2PC M ulti Fast M DCC 2PC M ulti Fast M DCC 2PC M ulti Fast M DCC 2PC M ulti Fast M DCC Commits/Aborts (in thousands) Hotspot Size Commits Aborts 2% 5% 10% 20% 50% 90% 0 200 400 600 800 1000 Response Times (ms) Figure 6. Commits/aborts for varying conflict rates Fi ma Phase 1). The experiment ran for 3 minutes af warm-up. Figure 5 shows the cumulative dist tions (CDF) of response times of the successfu The median response times are: 245ms 17
23. マイクロベンチマーク: ローカリティの影響 リーダーがローカルのノードである行にアクセスする割合を変化させ，その影響を調査． • ローカリティが 100 % の場合，MDCC (Multi) のコミ ット遅延が低いが，ローカリティが 80 % 以下の場 合，MDCC (Full) のコミット遅延が低い． • 最大コミット遅延は MDCC (Multi) の方が大きい． MDCC (Multi) では，リーダーで直列化するためキュ ーイングが発生． MDCC (Full) は高速パスで並列に提案が処理される． 0 10 20 30 40 50 60 70 80 2PC M ulti Fast M DCC 2PC M ulti Fast M DCC 2PC M ulti Fast M DCC 2PC M ulti Fast M DCC 2PC M ulti Fast M DCC 2PC M ulti Fast M DCC Commits/Aborts (in thousands) Hotspot Size Commits Aborts 2% 5% 10% 20% 50% 90% 0 200 400 600 800 1000 Multi MDCC Multi MDCC Multi MDCC Multi MDCC Multi MDCC Response Times (ms) Probability of Local Master 100% 80% 60% 40% 20% 0 100 200 300 400 500 Response Time (ms) Figure 6. Commits/aborts for varying conflict rates Figure 7. Response times for varying master locality Fig tim Phase 1). The experiment ran for 3 minutes after a 1 minute warm-up. Figure 5 shows the cumulative distribution func- tions (CDF) of response times of the successful transactions. The median response times are: 245ms for MDCC, independent of transac Fast Paxos, collisions a collision/conflict occ not agree on the same 18
24. Conclusion
25. 結論 • マルチ DC 環境でトランザクションのコミット遅延を削減するために新たなコミットプロ トコル MDCC (Multi-Data Center Consistency) を提案． • 行ごとに Generalized Paxos を実行し，トランザクションの可換性を活用しながら高速ク ォーラムでのコミットを試みることで，通常 1 RTT のコミット遅延を実現． • クォーラムベースのシステムでドメイン制約を保証する手法を初めて実現． • 2PC や Megastore と比較してコミット遅延を約 50 % 削減，ログレプリケーションのボト ルネックを解消してスケーラビリティを向上． 19
26. 参考文献 (1) [1] Tim Kraska et al. MDCC: Multi-data center consistency. In Proc. EuroSys ’13, page 113–126, 2013. [2] Jason Baker et al. Megastore: Providing scalable, highly available storage for interactive services. In Proc. CIDR ’11, pages 223–234, 2011. [3] James C. Corbett et al. Spanner: Google’s globally-distributed database. In Proc. OSDI’12, page 251–264, 2012.
27. 参考文献 (2) [4] Stacy Patterson et al. Serializability, not serial: Concurrency control and availability in multi-datacenter datastores. Proc. VLDB Endow., 5(11):1459–1470, 2012. [5] Leslie Lamport. Fast Paxos. Distrib. Comput., 19(2):79–103, 2006. [6] Leslie Lamport. Generalized consensus and Paxos. Technical Report MSR-TR-2005-33, Microsoft Research, 2004.
28. 参考文献 (3) [7] Fay Chang et al. Bigtable: A distributed storage system for structured data. ACM Trans. Comput. Syst., 26(2), 2008.