Approximation algorithms for semidefinite packing problems with applications to maxcut and graph coloring

Authors:
G. Iyengar;D. J. Phillips;C. Stein
Affiliations:
Department of IEOR, Columbia University, New York, NY;Department of IEOR, Columbia University, New York, NY;Department of IEOR, Columbia University, New York, NY
Venue:
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Year:
2005

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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.