CS262, Algorithms and Data Structures, Fall 2009
Linear Programming and Approximation Algorithms


 

Instructor: Marek Chrobak, Engineering II 406, x3769, marek@cs.ucr.edu.

Office hours: Monday 2-4PM, or by appointment.

Schedule: TT 8:10-9:30AM Sproul 2212

Syllabus: In this class we will discuss approximation algorithms for combinatorial optimization problems. The focus of the course will be on linear programming techniques, in particular on the role of the duality theory and various primal-dual methods for the design and analysis of efficient approximation algorithms. We will cover both off-line and on-line algorithms.

This is an advanced class and students are expected to possess some prerequisite knowledge required to follow the material. Strong background on algorithm design and analysis is required, including the following topics: divide-and-conquer, dynamic programming, algorithms on graphs, shortest paths, minimum spanning trees, maximum flow, bipartite matching, amortized analysis. Some prior exposure to linear programming and/or to approximation algorithms is strongly recommended. In terms of prerequisite coursework, an advanced undergraduate class on algorithms is required, and a graduate course recommended. If you are not sure if you have the background needed to take this class, please see the instructor.

The class will be taught in the standard seminar format. During the first several weeks, the instructor will present an overview of the area and cover basic facts about linear programming, duality, and some basic applications of the primal-dual to the design of approximation algorithms. The remainder of the class will consist of student presentations. A list of papers to present will be available, and students will be allowed to propose their own topics.

Each student will give a presentation. The expected time of a presentation will be 2 hours (about 1.5 lecture). At least a week prior to the scheduled presentation, a brief summary of the presentation, ideally about 5-6 pages long, needs to be submitted (LaTeX only). The summary should contain a rough content of the presentation, and should include some original material -- typically examples to illustrate concepts and ideas from the presented paper. Guidelines and a template for summary papers will be available. These papers must be well written and fully self-contained. They will be distributed to the whole class and other students are encouraged to critique them. There will be no tests. The grade will be based on the presentation(s), the presentation summary, attendance, and activity in class.

Topics (very tentative):

  Lectures


  List of Papers

Facility Location and k-Medians
  1. K.Jain, V.V.Vazirani, 1999, "Primal-dual approximation algorithms for metric facility location problems"
    (Not for a presentation -- I will present it myself)
  2. D.B.Shmoys, E.Tardos, K.I.Aardal, 1997, "Approximation algorithms for facility location problems"
    (Art Rakthanmanon)
  3. S.Guha, S.Khuller, 1998, "Greedy strikes back: improved facility location algorithms"
    (David Cohen)
  4. V.Arya, N.Garg, R.Khandekar, A.Meyerson, K.Mungala, V.Pandit, "Local search heuristics for k-median and facility location problems"
    (Changhui Lin)
  5. K.Jain, M.Mahdian, E.Markakis, A.Saberi, V.V.Vazirani, "Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP"
    (Peng Wang)
  6. M.Mahdian, Y.Ye, J.Zhang, "Approximation algorithms for metric facility location problems"
    (Kind of technical ...)
  7. J.Byrka, K.Aardal, "The approximation gap for the metric facility location problem is not yet closed"
    (Not for a full presentation -- only additional info)
  8. D.Fokakis, "A primal-dual algorithm for online non-uniform facility location"
    (Li Yan)

Steiner Networks
  1. D.Williamson, M.X.Goemans, M.Mihail, V.V.Vazirani, "A primal-dual approximation algorithm for generalized Steiner network problems"
Covering and Packing
  1. J.Mestre, Primal-dual approximation algorithm for partial vertex cover: making educated guesses
  2. N.Buchbinder, J.Naor, Online primal-dual algorithms for covering and packing problems

  About the Report Paper ...

  Resources

  Good causes (not related to class)