MFCS 2008: Mathematical Foundations of Computer Science 2008 pp 539-550 | Cite as
Approximating Independent Set and Coloring in Random Uniform Hypergraphs
Abstract
We consider the problems Independent Set and Coloring in uniform hypergraphs with n vertices. If \(\mathcal{NP} \not \subseteq \mathcal{ZPP}\), there are no polynomial worst case running time approximation algorithms with approximation guarantee n 1 − ε for any ε> 0. We show that the problems are easier to approximate in polynomial expected running time for random hypergraphs. For d ≥ 2, we use the H d (n,p) model of random d-uniform hypergraphs on n vertices, choosing the edges independently with probability p. We give deterministic algorithms with polynomial expected running time for random inputs from H d (n,p), and approximation guarantee O(n 1/2·p − (d − 3)/(2d − 2)/(ln n)1/(d − 1)).
Keywords
Random Graph Approximation Ratio Chromatic Number Random Input Color ClassisPreview
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