Reordering items at scale: From O(n) to O(1)

Transcript

3. 1,000+ books Sorted Numbered
4. Inserting a New Book 1. Initial state 2. A new book arrives 3. Conflict 4. Relabeling
5. Moving a Book: A → B 1. Initial state 2. Request move book 2 to 4 3. After book 2 is moved 4. Relabeling
6. Ignacio Chiazzo Cardarello Staff Engineer at Shopify @ignacio-chiazzo
7. Products Collections Ecommerce Example "Summer 2026", "Newest", "Clothing", . .. Shoes 99.9 usd
8. Entity diagram
9. Entity diagram
10. Entity diagram ~ Book's label
11. Simple right? This pattern is everywhere
12. This pattern is everywhere! • Ecommerce shopping list • Music Playlists • Kanban boards • Photos, Bookmarks, Menus ...
13. And it works great!
14. Until it breaks…
15. Sorting lists at scale Small List 1,000 items. Reorder one? up to 1,000 writes. Medium List 25,000 items. Reorder one? up to 25,000 writes. Large List N items. Reorder one? up to N writes.
17. The journey
18. Models Business Logic API
19. User Adoption
20. Monitors: Database Writes
21. New JOIN table Table A Table B Table C Table D Monitors: Database Writes per Table
22. Insert Reorder Found the problem! 󰡸 Writes per Operation
23. The timeline 1. Identified a problem Database writes Observed two bad patterns caused by Insert and Reorder. Established target and baseline. 2. Monitoring 3. Explore and Prototype Investigate
24. ~ O(1) Exploring a solution
25. ~ O(1) Exploring a solution
26. ~ O(1) Exploring a solution
27. Gap Running out of space
28. Gap Running out of space
29. Rebalance ~ old insert Running out of space
30. X 1 X 10 X 5 X 3 X 2 Bisections = Log 2 (Gap) Bisections
31. • Integers (consecutive numbers) 1, X, 2 ❌ • Decimal 1, 1.5, 2 ✅ • Big int 1000, 1500, 2000 ✅ • String aa, ab, ac ✅ Data Types: Exploring a Solution
32. • Storage Size: Fixed vs Variable • # Bisections before rebalance: Log₂(Gap) • Performance on reads & writes • Development cost Data Types: Exploring a Solution
33. • Lexicographically ranking system developed by Atlassian. • The Format "0 | aaab", "0 | aaac" • When no room: extend the string length or rebalance (e.g., "aa" and "ab" -> "aai") • Rebalance: no room, strings too long, and periodically. Strings with optimizations - Lexorank Rebalancing
34. Example: 3 Buckets: 🟢 Active → 📥 Destination | 💤 Spare Lexorank - Rebalance with buckets *The example is illustrative, it uses a few digits for simplicity Before (Bucket 0 — cramped): 😫 no room 0|aa 0|ae 0|aaj 0|aaji 0|aajii Bucket 0
35. Example: 3 Buckets: 🟢 Active → 📥 Destination | 💤 Spare Lexorank - Rebalance with buckets *The example is illustrative, it uses a few digits for simplicity Before (Bucket 0 — cramped): Bucket 0 😫 no room
36. Example: 3 Buckets: 🟢 Active → 📥 Destination | 💤 Spare Lexorank - Rebalance with buckets *The example is illustrative, it uses a few digits for simplicity Before (Bucket 0 — cramped): During migration (0 —> 1): Bucket 0 Bucket 1 After migration (Bucket 1): Bucket 1 Bucket 0 Bucket 0 😫 no room
37. Optimizations • The element size is variable. It depends on the list size. • The Gap is variable and unevenly distributed. • Optimized for usage patterns. • API optimization. Thanks to P. Racicot, A. Richner, A. Pham, M. Ariss, E. Rumley & I. Chepelev for their optimization contributions!
38. Move request (2 , 3) → 4 == (4→ 2) Optimizing User Requests
39. New algorithm Released Performance Impact
40. Observed two bad patterns caused by Insert/Reorder Established target and baseline. The timeline 1. Identified a problem 2. Monitoring Database writes 5. Measure the impact Compare with target 3. Explore and Prototype Investigate Do things; Tell people! 4. Implementation Ship, ship, ship! # alerts, tests, etc. 6. Prevent degradation
41. Ignacio Chiazzo ignacio-chiazzo Key Takeaways • Simple problems become hard problems at scale. • Using Integers works well for small lists, but they don't scale. • The six-step framework applies to any performance problem. • And now you know why the AI asked for the list size.
42. Ignacio Chiazzo ignacio-chiazzo Thanks