Algorithms and Data Structures (block course)

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.

Registration

You need to register on this webpage to get access to exercise sheets and other course material.

Exams

You grade will be determined by a written exam. Admittance to the exams requires active participation in the course.

Endterm: tba

Re-Exam: tba

Prerequisites

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

Date	Lecturer	Topic	Comment
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

Literature