The problem sets will be available online, on this page.

  • randomized algorithms
  • algorithms for strings
  • numerical algorithms
  • approximation algorithms
  • linear programming
  • parametric search
  • hashing
  • complexity theory and lower bounds
  • Friday, 21.04.2017
    • Administrativa
    • Introduction
    • Recap linear programming
    • Duality of linear programs
  • Monday, 24.04.2017 (lecture given by Katharina Klost)
    • Ellipsoid-algorithm
  • Friday, 28.04.2017 (lecture given by Katharina Klost)
    • Ellipsoid-Algorithm
    • Duality
    • Proof of strong duality using Farkas Lemma
  • Fiday, 05.05.2017
    • Fourier-Motzkin elimination
    • Proof of Farkas Lemma via Fourier-Motzkin elimination
  • Monday, 08. May 2017
    • Two Player-Zero Sum Games and von Neumann's Minimax-Theorem
  • Friday, 12. May 2017
    • The complexity class PPAD
    • Randomized Algorithms: MST
  • Monday, 15. May 2017
    • Randomized Algorithms: MST
  • Friday, 19. May 2017
    • KKT-algorithm for MST: Analysis
    • Notes
  • Monday, 22. May 2017
    • Cuckoo-Hashing
  • Friday, 26. May 2017
    • Encoding Arguments
    • Analysis of Cuckoo-Hashing
  • Monday, 29. May 2017 (lecture given by Katharina Klost)
    • Approximation algorithms
    • Set Cover
    • Inapproximability of the TSP
  • Friday, 02. June 2017
    • Cuckoo-Hashing: Addendum
    • Metric TSP: Tree heuristic
  • Tuesday, 06. June 2017
    • Metric TSP: Christofides
    • Euclidean TSP: Arora's PTAS
  • Monday, 12. June 2017
    • Euclidean TSP: Arora's PTAS
      • Nice instances
      • Portal-respecting tours
      • Portal-respecting tours with at most two crossings
  • Friday, 16. June 2017
    • Euclidean TSP: Arora's PTAS
      • Portal-respecting tours using each portal at most twice
      • Plane portal-respecting tours using each portal at most twice
      • Finding an optimal portal-respecting tour
      • Transformation of an optimal tour into a portal-respecting tour
  • Tuesday, 20. June 2017
    • Euclidean TSP: Arora's PTAS
      • Transformation of an optimal tour into a portal-respecting tour
      • Random shifting
      • Wrap-up of the analysis
  • Friday, 23. June 2017
    • Parametrized algortihms
    • A singly exponential algorithm for vertex cover
    • Problems on trees and tree-like graphs
  • Monday, 26. June 2017
    • Tree-width: definition and properties
  • Friday, 30. June 2017
    • Tree-width: algorithmic applications
  • Monday, 03. July 2017
    • k-linked sets and tree-width
  • Friday, 07. July 2017
    • finding a tree decomposition of a graph
  • Monday, 10. July 2017
    • Complexity theory inside P: SETH and OV
  • Friday, 14. July 2017
    • SETH-hardness of Fréchet distance
  • Monday, 17. July 2017
    • SETH-hardness of Fréchet distance (continued)
  • Friday 21. July 2017 (09:00–12:00, Room 112)
    • oral exam
  • Monday 16. October 2017 (plan, 14:00–16:00, Room 112)
    • second oral exam

References

Recommended Prerequisites

Tou pass the class, you have to

The successful participation in the exercises and passing the final exam are independent of each other.

This class is graded. The final grades are based exclusively on the final exam. There will be an oral exam at the end of the semester, and a make up exam in October. The oral exam takes place on Friday, July 21, 9:00–15:00 in room 112. Please sign up one week in advance.

The class takes place Monday, 10–12, in SR 005 and Friday, 10–12, in SR 046, the exercises take place Tuesday, 16–18, SR 051. The exercises are conducted by Katharina Klost.

Office hours: Tuesday, 14–15, in room 112 and by appointment.

The problem sets are published on this site on a weekly basis. They will appear only online. The regular period for solving the problems is from Friday to Monday, 10 days later. The solutions have to returned in class. Please work in groups of two.

Problem sets that are handed in after the due date receive no credit.

No.OutDue pdftexRemarks
1 01.04.2017 26.04.2017  
2 22.04.2017 02.05.2017 English version: [pdf] [tex]
3 28.04.2017 08.05.2017  
4 05.05.2017 15.05.2017  
5 12.05.2017 22.05.2017  
6 19.05.2017 29.05.2017  
7 26.05.2017 06.06.2017 Problem 1b) has been updated.
8 02.06.2017 12.06.2017  
9 09.06.2017 19.06.2017  
10 16.06.2017 26.06.2017 Problem 3 has been updated.
11 23.06.2017 03.07.2017  
12 30.06.2017 10.07.2017 penultimate problem set
13 07.07.2017 17.07.2017 last problem set
Impressum