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Algorithms and Data Structures (block course)
The course will cover basic and advanced data structures and algorithms, as well as their analysis. Examples of data structures are perfect hashing, splay trees, randomized search trees, union-find structures. In terms of problem domains, we cover graphs, strings, polynomials, and geometry. Furthermore, we discuss algorithm analysis techniques such as amortization and randomization, and general algorithm design principles.
Time, Date, and Format
This core course will be offered in an intensive block version between February 28 and March 26. The course can be taken only in presence.
The format of the course will be as follows: A "unit" consists of a 70 minute lecture, followed by 2 hours of group work on an exercise sheet, followed by a short discussion section with a tutor (tutorial). Typically we will have two units a day, the first starting at 9am, the second at 2pm, Monday through Friday, except for Wednesdays, which will have only the morning unit. As an exception, the first lecture happens on February 28 at 14:00. See Information→Timetable for details.
The lecture will take place in room HS003 in building E1 3.
The tutorial will take place at 12:00 and at 17:00 in seminar room SR016 in building E1 3. The rooms 016 in building E1 3 and 106 in building E1 1 are reserved throughout the whole lecture period as working space.
This will be a very intensive course. Do not plan on doing anything else serious beside it.
You need to register on this webpage to get access to exercise sheets and other course material.
You grade will be determined by a written exam. Admittance to the exams requires active participation in the course.
The course requires basic knowledge in algorithms and data structures as covered for example by the course “Introduction to Algorithms and Data Structures” (“Grundzüge von Algorithmen und Datenstrukturen”). In particular, you should be familiar with correctness proofs of algorithms. Specific concepts that you should have basic familiarity with and should be able to apply include:
- pseudocode notation
- O-notation, running time analysis
- binary search
- basic sorting algorithms (e.g. mergesort)
- arrays, linked lists
- stacks, queues
- heaps / priority queues
- binary search trees, balanced binary search trees (e.g. AVL trees)
- definition of a graph
- graph traversal (e.g. depth first search / breadth first search)
In case you want to read up on these topics we recommend the videos of the course “Introduction to Algorithms and Data Structures”, see Information→Materials.
Tentative List of Topics
- greedy algorithms
- dynamic programming
- divide and conquer (e.g. master theorem, integer multiplication, FFT)
- randomized algorithms (e.g. quicksort, randomized search trees, hashing)
- amortization (e.g. Fibonacci heaps, union find)
- strings (e.g. pattern matching, tries)
- graphs (e.g. shortest paths, maxflow, matching)
- computational geometry
|28.2. 2pm||Intro: machine model, O-notation|
|29.2. 9am||Greedy and Dynamic Programming I|
|29.2. 2pm||Dynamic Programming II|
|1.3. 9am||Divide and Conquer I: basic examples, master theorem|
|1.3. 2pm||Divide and Conquer II: Strassen, Karatsuba|
|4.3. 9am||Divide and Conquer III: Toom-Cook, FFT|
|4.3. 2pm||Divide and Conquer IV: applications of FFT|
|5.3. 9am||Randomized I: model, quicksort, rank select|
|5.3. 2pm||Randomized II: dictionaries, randomized search trees, treaps|
|6.3. 9am||Randomized III: hashing|
|7.3. 9am||Randomized IV: more on hashing|
|7.3. 2pm||Randomized V: algorithms that work with high probability|
|8.3. 9am||Amortization I: intro|
|8.3. 2pm||Amortization II: Fibonacci heaps / hollow heaps|
|11.3. 9am||Amortization III: splay trees|
|11.3. 2pm||Amortization IV: union find|
|12.3. 9am||Strings I: longest common subsequence|
|12.3. 2pm||Strings II: string matching: Rabin-Karp, Knuth-Morris-Pratt|
|13.3. 9am||Strings III: string matching continued, tries|
|14.3. 9am||Strings IV: suffix trees|
|14.3. 2pm||Graphs I: intro, BFS+DFS, Dijkstra|
|15.3. 9am||Graphs II: shortest path: Bellman-Ford, Floyd-Warshall, Johnson, ...|
|15.3. 2pm||Graphs III: more shortest paths|
|18.3. 9am||Graphs IV: minimum spanning tree|
|18.3. 2pm||Graphs V: maxflow: intro, maxflow mincut|
|19.3. 9am||Graphs VI: maxflow: Ford-Fulkerson|
|19.3. 2pm||Graphs VII: maxflow: blocking flows|
|20.3. 9am||Graphs VIII: maximum matching|
|21.3. 9am||Graphs IX: global mincut|
|21.3. 2pm||Geometry I: intro, convex hull|
|22.3. 9am||Geometry II: convex hull ctd., orthogonal range searching|
|22.3. 2pm||Geometry III: orthogonal range searching ctd.|
|25.3. 9am||Geometry IV: sweep line|
|25.3. 2pm||Geometry V: Voronoi diagrams|
|26.3. 9am||Teaser: SAT Algorithms|
|26.3. 2pm||Teaser: Fine-Grained Complexity|
The course will not follow a particular book. The following is a list of literature that could be useful.
- [MS] K. Mehlhorn, P. Sanders: Algorithms and Data Structures - The Basic Toolbox, Springer, 2008 (ISBN: 9783540779773)
- [CLRS] T. H. Cormen, C. E. Leiserson, R. L. Rivest, C. Stein, Introduction to Algorithms - Second Edition, McGraw-Hill, 2001 (ISBN: 0262531968)
- [KT] J. Kleinberg and E. Tardos, Algorithm Design, Addison Wesley, 2005 (ISBN: 0-321-29535-8)
- [Meh] K. Mehlhorn, Data Structures and Algorithms, Vols. 1-3, Springer Verlag, 1984
- [Koz] D. Kozen, The Design and Analysis of Algorithms, Springer Verlag, 1991
- [GKP] R. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics, Addison-Wesley, 1994
- [CR] M. Crochemore, W. Rytter, Text Algorithms, Oxford University Press, 1994
- [Sch] A. Schrijver, A Course in Combinatorial Optimization, 2013
- [BKOS] M. de Berg, M. van Kreveld, M. Overmars, O. Schwarzkopf, Computational Geometry, Springer Verlag, 2000
- [Eri] J. Erickson, Algorithms, 2019 (Free electronic version)