Flexible coloring

Motivated b y reliability considerations i n data deduplication for s torage s ystems, w e introduce the problem of flexible coloring. Given a hypergraph H and the number of allowable colors k, a exible coloring o f H is a n assignment o f o ne or more colors to each vertex s uch that, for each hyperedge, i t is possible to choose a color from each vertex's color list so that this hyperedge i s strongly colored (i.e., each vertex has a different color). Different colors for the same vertex can be chosen for di fferent i ncident hyperedges ( hence the term flexible). The goal is to minimize color consumption, namely, the total number of colors assigned, counting multiplicities. Flexible coloring is N P-hard and trivially approximable, w here s is t he size o f t he l argest hyperedge, and n is the number of vertices. Using a recent result by Bansal and K hot, we show that if k is constant, then it is UGC-hard to approximate to within a factor of s ɛ, for arbitrarily small constant ɛ > 0. Lastly, we present an algorithm with an approximation ratio, where k' is number of colors used by a strong coloring algorithm for H. External Posting Date: March 11, 2011 [Fulltext] A pproved for External Publication Internal Posting Date: March 11, 2011 [Fulltext] Additional Publication Information: to be published in Information Process Letters.  Copyright 2011 Hewlett-Packard Development Company, L.P.