Approximation Algorithms for Semidefinite Packing Problems with Applications to Maxcut and Graph Coloring

  • G. Iyengar
  • D. J. Phillips
  • C. Stein
Conference paper

DOI: 10.1007/11496915_12

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3509)
Cite this paper as:
Iyengar G., Phillips D.J., Stein C. (2005) Approximation Algorithms for Semidefinite Packing Problems with Applications to Maxcut and Graph Coloring. In: Jünger M., Kaibel V. (eds) Integer Programming and Combinatorial Optimization. IPCO 2005. Lecture Notes in Computer Science, vol 3509. Springer, Berlin, Heidelberg

Abstract

We describe the semidefinite analog of the vector packing problem, and show that the semidefinite programming relaxations for Maxcut [10] and graph coloring [17] are in this class of problems. We extend a method of Bienstock and Iyengar [5] which was based on ideas from Nesterov [25] to design an algorithm for computing ε-approximate solutions for this class of semidefinite programs. Our algorithm is in the spirit of Klein and Lu [18], and decreases the dependence of the run-time on ε from ε− − 2 to ε− − 1. For sparse graphs, our method is faster than the best specialized interior point methods. A significant feature of our method is that it treats both the Maxcut and the graph coloring problem in a unified manner.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • G. Iyengar
    • 1
  • D. J. Phillips
    • 1
  • C. Stein
    • 1
  1. 1.Department of IEORColumbia UniversityNew York

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