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Algorithms and Data Structures (block course)
The course will cover basic and advanced data structures & algorithms and their analysis. Examples of data structures are cuckoo 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 & Format
This core course will be offered in an intensive block version between February 28 and March 25. We strongly recommend that you participate in this course being present in the classroom. However, we also make it possible to take the course remotely, see Information->Virtual Guide.
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 all Wednesdays, which will have only the morning unit.
The lecture will usually take place in room HS II in building E2 5. However, on some exceptions we change to different rooms, for details see Information->Timetable or see the list of topics below.
The tutorial will take place at 12:00 and at 17:00 in seminar room 014 in building E1 3. The seminar rooms 014 and 015 in building E1 3 are reserved throughout the whole lecture period as working spaces.
For information how to join the lecture or tutorial virtually, see Information->Virtual Guide.
This will be a very intensive course. Do not plan on doing anything else serious beside it.
Your final grade will be determined by your performance on a midterm exam (35%) and a final exam (65%). There will be a repeat exam for the final. Admittance to the exams requires active participation in the course.
Midterm: 11.3. 14:00-17:00 GHH lecture hall
Endterm: 31.3. 16:30-19:00 GHH lecture hall
Re-Exam: 13.4. 16:00-19:00 HS002 E1 3
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 script 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)
- (high-dimensional) geometry
|28.2. 9am||RS||Intro: machine model, O-notation|
|28.2. 2pm||RS||Divide and Conquer I: basic examples, master theorem|
|1.3. 9am||RS||Divide and Conquer II: Strassen, Karatsuba|
|1.3. 2pm||RS||Divide and Conquer III: Toom-Cook, FFT|
|2.3. 9am||RS||Divide and Conquer IV: applications of FFT|
|3.3. 9am||KB||Randomized I: model, quicksort, rank select||room change: HS002 E1 3|
|3.3. 2pm||KB||Randomized II: dictionaries, randomized search trees, treaps||room change: HS III E2 5|
|4.3. 9am||KB||Randomized III: hashing||room change: HS002 E1 3|
|4.3. 2pm||KB||Randomized IV: more on hashing|
|7.3. 9am||RS||Amortization I: intro||room change: HS III E2 5|
|7.3. 2pm||RS||Amortization II: Fibonacci heaps / hollow heaps|
|8.3- 9am||RS||Amortization III: splay trees|
|8.3. 2pm||RS||Amortization IV: union find|
|9.3. 9am||KB||Strings I: DP for LCS|
|10.3. 9am||KB||Strings II: string matching: Rabin-Karp, Knuth-Morris-Pratt|
|10.3. 2pm||KB||Strings III: string matching continued, tries|
|11.3. 9am||KB||Strings IV: suffix trees|
|11.3. 2pm||Midterm Exam||GHH lecture hall|
|14.3. 9am||RS||Graphs I: intro, BFS+DFS, Dijkstra|
|14.3. 2pm||RS||Graphs II: shortest path: Bellman-Ford, Floyd-Warshall, Johnson, ...|
|15.3. 9am||RS||Graphs III: more shortest paths|
|15.3. 2pm||RS||Graphs IV: minimum spanning tree|
|16.3. 9am||KB||Graphs V: maxflow: intro, maxflow mincut|
|17.3. 9am||KB||Graphs VI: maxflow: Ford-Fulkerson|
|17.3. 2pm||KB||Graphs VII: maxflow: blocking flows|
|18.3. 9am||KB||Graphs VIII: maximum matching|
|18.3. 2pm||KB||Graphs IX: global mincut|
|21.3. 9am||RS||Geometry I: orthogonal range searching|
|21.3. 2pm||RS||Geometry II: sweep|
|22.3. 9am||RS||Geometry III: point sets viewed globally|
|22.3. 2pm||RS||Geometry IV: point sets viewed locally|
|23.3. 9am||RS||Geometry V: arrangements, duality||room change: HS002 E1 3|
|24.3. 9am||KB||SAT Algorithms||room change: HS001 E1 3|
|24.3. 2pm||KB||Teaser: Fine-Grained Complexity|
|25.3. 9am||KB||Teaser: Streaming and Sketching I||room change: HS002 E1 3|
|25.3. 2pm||KB||Teaser: Streaming and Sketching II|
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)