Index management in shallow depth Andrea Giuliano @bit_shark 

Architecture of a DBMS Andrea Giuliano @bit_shark 

Disk manager The disk manager provides the following commands for a page • allocate a page • deallocate a page • read a page • write a page The size of a page is chosen to be the size of a disk block and pages are stored as disk blocks so that reading or writing a page can be done in one disk I/O Andrea Giuliano @bit_shark 

Buffer manager is the software layer responsible for bringing pages from disk to main memory as needed and manages the available main memory by partitioning it into a collection of pages the buffer pool Andrea Giuliano @bit_shark 

Mysql indexes are stored! in B-trees 

B-tree structure data entry: record stored in an index file data record: record stored in a database file Andrea Giuliano @bit_shark 

Clustered index data entries and data records have the same (or close) order Andrea Giuliano @bit_shark 

Unclustered index data entries and data records have the different order criteria Andrea Giuliano @bit_shark 

Dense index An index is dense if every value of the search key that appears in the data file appears also in at least one data entry of the index Andrea Giuliano @bit_shark 

An index is sparse if every value of the search key that appears in the data entry points to a page of the data record Sparse index Andrea Giuliano @bit_shark 

Search in a b-tree Cost: logF n fan-out n leaves Andrea Giuliano @bit_shark 

Insert and delete ..too deep Insert and delete operations must keep the tree balanced towards split, redistribution and coalesce techniques. Andrea Giuliano @bit_shark 

How can I compute I/O accesses? Andrea Giuliano @bit_shark 

ask for code, author, publisher af all books with a given cost how many page accesses do we need to answer to the query? Book case Query: • 2.000.000 records (tuples) • 200.000 pages • 10 data record in a page • 200 records with the same value of the attribute cost (on average) • dense non-clustering B+-tree index with search key cost BOOK code author cost publisher Andrea Giuliano @bit_shark 

Let’s build the index structure ! • we know that each tuple has 4 field so in each page there are 40 fields • we can infer that 20 data entries fit in one leaf page of the index • so we have a fan-out of 20 Book case • 2.000.000 records (tuples) • 200.000 pages • 10 data record in a page • 200 records with the same value of the attribute cost (on average) • dense non-clustering B+-tree index with search key cost BOOK code author cost publisher Andrea Giuliano @bit_shark 

We know there is an occupancy factor of 67% we have 13 data entries in the leaves (each of which can contain 20 data entries) How many leaves are there in the tree?
 2.000.000/13 = 153.846 leaves Book case … fan-out: 20 Andrea Giuliano @bit_shark 

There are 153.846 leaves In order to go to the leaves we need Book case log20 (153.846) = 4 I/O page accesses … fan-out: 20 Andrea Giuliano @bit_shark 

Book case Remember, we have on average 200 records with the same value of the attribute cost therefore 200/13 = 15 pages (on average)
 We need to visit these leaves because the index is dense and for each tuple we have to access the 200 data record in order to obtain the other attributes … fan-out: 20 Andrea Giuliano @bit_shark 

The total cost is: 
 4 + 15 + 200 = 219 I/O accesses Book case ~ 3 sec … fan-out: 20 Andrea Giuliano @bit_shark 

• 2.000.000 records (tuples) • 200.000 pages • 10 data record in a page • 200 records with the same value of the attribute cost (on average) • sparse clustering B+-tree index with search key cost ask for code, author, publisher af all books with a given cost how many page accesses do we need to answer to the query? BOOK code author cost publisher Book case Query: Andrea Giuliano @bit_shark 

Let’s build the index structure ! • we know that each tuple has 4 field so in each page there are 40 fields • we can infer that 20 data entries fit in one leaf page of the index • so we have a fan-out of 20 Book case • 2.000.000 records (tuples) • 200.000 pages • 10 data record in a page • 200 records with the same value of the attribute cost (on average) • sparse clustering B+-tree index with search key cost BOOK code author cost publisher Andrea Giuliano @bit_shark 

We know there is an occupancy factor of 67% we have 13 data entries in the leaves (each of which can contain 20 data entries)
 BUT each data entry points to a data record page (and not to a tuple) How many data record pages do we have?
 2.000.000/10 = 200.000 data record pages Book case … fan-out: 20 Andrea Giuliano @bit_shark 

We know there is an occupancy factor of 67% we have 13 data entries in the leaves (each of which can contain 20 data entries)
 BUT each data entry points to a data record (and not to a tuple) How many leaves there are in the tree?
 200.000/13 = 15.384 leaves Book case … fan-out: 20 Andrea Giuliano @bit_shark 

There are 15.384 leaves In order to go to the leaves we need Book case log20 (15.384) = 3 I/O pages accesses Remember, we have on average 200 data records with the same value of the attribute cost therefore 200/10 = 20 data record pages to visit … fan-out: 20 Andrea Giuliano @bit_shark 

The total cost is: 
 3 + 20 = 23 I/O accesses Book case ~ 0.3 sec … fan-out: 20 Andrea Giuliano @bit_shark 

And what if the attributes we want
 were part of the search key? Book case Andrea Giuliano @bit_shark 

In the worst case we have to visit all the 2.000.000 tuples Book case without index ~ 50 min Andrea Giuliano @bit_shark 

Ο λογος δηλοι οτι Think before doing 

? Thanks! Andrea Giuliano @bit_shark 

References: https://www.flickr.com/photos/james_wheeler/9340597900/sizes/o/in/photolist-fep1ko-bQByHk- duQ4Qr-82aKA9-82aL6y-8Tn6uc-iPzADZ-99etoQ-cZy6e9-jyqdnW-bxHjLf-8gP59X-cZDq3h-cZDq9d- cZDq8N-cZDq7d-cZDqwy-cZDqym-cZDqCf-cZDqAo-cZDqsS-cZDqnQ-cZDqey-cZDqkA-cZDqkJ- cZDqLh-7Dg8pp-a7f1QC-a7c8rK-7Dg7n6-gCbBVr-9FZ4J1-e6XCpX-aZnsGv-ecTv5D-atFACM- gjXozL-9LBjtC-knoEf8-8LGGqw-a8Hw3M-gvL3bp-a7gmG6-aju6p2- brQ76S-7Ckbm1-85XaXe-8JBcwN-9oYU3p-a3VsvR-atFAup/ http://www.woking.gov.uk/images/instances/00004A290FD4.C0A801BA.000079A7.0015.jpg http://assets.20bits.com/20080513/b-tree.png, http://dblab.cs.toronto.edu/courses/443/2014/basic-index/dense-index.png http://dblab.cs.toronto.edu/courses/443/2014/basic-index/sparse-index.png http://www.geeky-gadgets.com/wp-content/uploads/2008/10/insert-delete_cufflinks.jpg, http:// www.geeky-gadgets.com/wp-content/uploads/2008/10/insert-delete_cufflinks.jpg http://webhostinggeeks.com/blog/wp-content/uploads/2012/07/611157_small.jpg https://farm7.staticflickr.com/6237/6230474283_50d1f0f4ac_b.jpg, https://www.flickr.com/photos/ javiercosio/6230474283/sizes/l/in/photolist- auyNWp-9GRjnM-9GRjmZ-9GRjFz-9GRjvV-9GUcPq-9GRjz8-9GRjm4-9GUcTb-9GRjCt-9GUcQC-9GUcY m-9GRjZD-9GRk1Z-9GUcMU-9GUcGh-9GRjsg-9GRjYZ-9GRjTF-9GRjGe-9GRjNe-9GRjBz-9GUcNs-9GU d25-9GUcKS-9GRjPn-9GRjRg-9GUcBh-9GUcVf-9GUcxj-9GUcuu-brLe7G-e8s4Cw- fyi4Rj-83LyYW-83HuFg-83LyLm-83LzUY-83Htrv-83Hv2H-83LBBb-83LAg9-83LBhQ-83Hw8t-83HtKD-83H sYk-afT6uk-cwVhL1-ceVgGC-8tFezr-8SeW9d/