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New Tools for Graph Coloring Sanjeev Arora

Summary: New Tools for Graph Coloring
Sanjeev Arora
Rong Ge
Department of Computer Science and
Center for Computational Intractability,
Princeton University
How to color 3 colorable graphs with few colors is a problem of longstanding interest. The
best polynomial-time algorithm uses n0.2072
colors. There are no indications that coloring using
say O(log n) colors is hard. It has been suggested that lift and project based SDP relaxations
could be used to design algorithms that use n colors for arbitrarily small > 0.
We explore this possibility in this paper and find some cause for optimism. While the case
of general graphs is till open, we can analyse the Lasserre relaxation for two interesting families
of graphs.
For graphs with low threshold rank (a class of graphs identified in the recent paper of Arora,
Barak and Steurer on the unique games problem), Lasserre relaxations can be used to find an
independent set of size (n) (i.e., progress towards a coloring with O(log n) colors) in nO(D)


Source: Arora, Sanjeev - Department of Computer Science, Princeton University


Collections: Computer Technologies and Information Sciences