Data Structures I

I am teaching English version of the course Data Structures 1 [NTIN066] in the summer semester of 2020/2021.

Lectures are held every Wednesday from 9:00 [in room S5 if possible, otherwise online]. Sign up for recitations in SIS.

We will meet on Zoom, you should have received a Zoom link by e-mail. If you have not, check your spam folder and let me know. All lectures will be recorded and the videos posted here.

Please read the complete rules of the game.

date topics sources video
3. 3. Introduction: what is a data structure – interface vs. implementation, static vs. dynamic, model of computation. Examples of interfaces: queue, set, ordered set, dictionary. Flexible arrays (with both stretching and shrinking). [L01] video board
10. 3. Different approaches to amortized analysis: aggregation, accounting, coins, potentials. Examples: binary counters, deletion using tombstones, lazily balanced BB[α] trees. [L01] video board
17. 3. Splay trees: amortized analysis of the Splay operation. Incorporating splaying in Find, Insert, and Delete. [L02] [ST] video board
24. 3. Splay trees: Complexity of BST operations; remarks on static and dynamic optimality, sequential traversal, and working set bound. (a,b)-trees: definition, logarithmic height, Find, Insert, Delete, choice of parameters. [L02] [L03] video board
31. 3. (a,b)-trees: Amortized bounds for (a,2a-1) and (a,2a)-trees. Top-down splitting and joining. Memory hierarchy: theoretical models – I/O, cache-aware, cache-oblivious. Examples: cache effects on a real machine, sequential scanning of arrays. [L03] [L05] [CO] video board
7. 4. Cache-oblivious algorithms. Sorting: MergeSort, multi-way MergeSort, a remark on FunnelSort and lower bounds. Matrix transposition: cache-aware tiling, cache-oblivious divide & conquer algorithm. [L05] [CO] video board
14. 4. Cache-oblivious model versus reality: Sleator-Tarjan theorem on competitivity of LRU. Hashing: buckets with lists (chaining). Choice of hash functions: c-universal systems of functions, expected bucket size, time complexity of hashing with chains. [L05] [CO] [STb] [L06] video board
21. 4. Hash function families: k-independence, constructions of universal/independent systems from linear functions. Generic bounds for composition of families, k-independent hashing from polynomials, tabulation hashing. Cuckoo hash tables. [L06] [Tb] [E10] video board
28. 4. Hash tables: open addressing, analysis of linear probing. [L06] [T] video board
5. 5. Hashing: lemmata on composition of hash function families. Hashing of vectors using scalar products. Bloom filters: 1-band, k-band. [L06] [Tb] video board
6. 5. Material covered at exercise classes: Hashing of vectors and strings using polynomials, rolling hashes. [L06] video board
12. 5. No lecture today – it's the rector's sporting day.
13. 5. Material covered at exercise classes: Plan: Optimization of Bloom filters, counting filters. [L06]
19. 5. Plan: Multi-dimensional data structures. Range queries on binary search trees. K-d trees: basic principle, lower bound. Range trees: construction, queries, dynamization by partial rebuilds, speedup by fractional cascading. [L07] [M7]

Assignments

Description of assignments can be found in ReCodEx. You need to create an account there and sign up to a group for the recitations you chose.

Additional material (especially source code) is available as a Git repository. You can also browse it on the web.

Please submit your solutions to ReCodEx.

Literature

This page is maintained by Martin Mareš