Data Structures 2
I am teaching Data Structures II [NTIN067] in the summer semester of 2023/2024.
The lectures will be on Mondays from 15:40 in S8.
If you want to consult anything, please write an e-mail to mares+ds@kam.mff.cuni.cz and we will discuss possibilities.
datum | topics | sources | recording |
---|---|---|---|
19. 2. | Static dictionary problem. FKS perfect hashing built from universal systems of hash functions. HMP hashing: reduction of universe to polynomial (just sketch) and then to quadratic (n-ary trie). | [P01] [FKS] [S2.1] | |
26. 2. | No lecture today. | ||
4. 3. | Deterministic static dictionaries: principle of permuting points in a grid, application to construction of HMP perfect hashing. Randomized construction of row permutations, derandomization using conditional expectation. | [P01] [HMP] | video [partial sound] |
11. 3. | A remark on sorting of reals. Structures for ordered sets of integers: van Emde-Boas trees based on recursive subdivision to buckets. A trick for implicit initialization of memory. vEB interpreted as a binary range tree: easier, but with slower updates. | [P02] [G] [E11] | video [bad sound] |
18. 3. | Generalized vEB trees: storing just ones (x-fast tries), speedup by indirection (y-fast tries). Heaps: binary, d-regular. Binomial trees and a sketch of binomial heaps. | [P02] [E11] [D4] | video |
25. 3. | Heaps: Binomial, lazy binomial, Fibonacci. | [D4] | video |
1. 4. | No lecture today: Ēostre, Paasfees, Великден, Ülestõusmispühad, Πάσχα, Páskar, 復活祭, Pace. | — | |
8. 4. | Splay trees: weighted analysis, static optimality, static finger bound, working set bound, hypothesis on dynamic optimality. | [D2.3] [STb] | video |
15. 4. | Introduction to data structures for graphs. Representation of static paths based on range trees with lazy propagation of updates. Heavy-light decomposition of trees. Link-Cut trees: interface, idea of thick-thin decomposition. | [P03] | video |
22. 4. | Plan: Link-cut trees: dynamic decomposition based on interconnected Splay trees. Application on Dinitz's maximum flow algorithm. Intermezzo: Static structure for interval evaluation of an associative operation. | [P03] [STa] [STb] |
Course material
Previous runs of the lecture:
- 2022 (English, includes video recordings)
- 2020 (Czech, includes video recordings)
- 2016 (Czech, includes video recordings)
- 2018 (Czech)
Literature:
- [D] Martin Mareš: Lecture notes on data structures
- [E] Erik Demaine: přednáška Advanced Data Structures z MIT
- [EC] Erik Demaine: Cache-Oblivious Algorithms and Data Structures (lecture notes)
- [G] Martin Mareš: Krajinou grafových algoritmů (Czech)
- [H] Handbook of Data Structures and Applications (accessible online from university network)
- [P] Martin Mareš: My notes (scanned, Czech)
- [S] Martin Mareš: The Saga of Minimum Spanning Trees, PhD Thesis at MFF UK, 2008
- [DS] Driscoll, Sarnak, Sleator, Tarjan: Making Data Structures Persistent, Proceedings of STOC, 1986
- [FKS] Fredman, Komlós, Szemerédi: Storing a Sparse Table with O(1) Worst Case Access Time, Journal of ACM, 1984
- [HMP] Hagerup, Miltersen, Pagh: Deterministic Dictionaries, Journal of Algorithms, 2001
- [M] Kurt Mehlhorn: Data Structures and Algorithms (digital version of the book)
- [MP] Michal Pokorný: Practical Data Structures, bachelor thesis at MFF UK, 2015
- [MS] Milan Straka: Functional Data Structures and Algorithms, PhD thesis at MFF UK, 2013
- [SE] Seidel: Union Find (lecture slides)
- [STa] Sleator, Tarjan: A Data Structure for Dynamic Trees, Journal of Computer and System Sciences, 1983
- [STb] Sleator, Tarjan: Self-Adjusting Binary Search Trees, Journal of the ACM, 1985
- [TL] Tarjan, van Leeuwen: Worst-Case Analysis of Set Union Algorithms, Journal of the ACM, 1984 (original analysis, not used at our lecture)