Abstract
Given a hypergraph and a set of colors, we want to find a vertex coloring to minimize the size of any monochromatic set in an edge. We give deterministic polynomial time approximation algorithms with performances close to the best bounds guaranteed by existential arguments. This can be applied to support divide and conquer approaches to various problems. We give two examples. For deterministic approximate DNF counting, this helps us explore the importance of a previously ignored parameter, the maximum number of appearance of any variable, and construct algorithms that are particularly good when this parameter is small. For partially ordered sets, we are able to constructivize the dimension bound given by Füredi and Kahn [].
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