Approximation Algorithms for Semidefinite Packing Problems with Applications to Maxcut and Graph Coloring
- 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
We describe the semidefinite analog of the vector packing problem, and show that the semidefinite programming relaxations for Maxcut  and graph coloring  are in this class of problems. We extend a method of Bienstock and Iyengar  which was based on ideas from Nesterov  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 , 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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