Coloring k-Colorable Semirandom Graphs in Polynomial Expected Time via Semidefinite Programming
The analysis of algorithms on semirandom graph instances intermediates smoothly between the analysis in the worst case and the average case. The aim of this paper is to present an algorithm for finding a large independent set in a semirandom graph in polynomial expected time, thereby extending the work of Feige and Kilian . In order to preprocess the input graph, the algorithm makes use of SDP-based techniques. The analysis of the algorithm shows that not only is the expected running time polynomial, but even arbitrary moments of the running time are polynomial in the number of vertices of the input graph. The algorithm for the independent set problem yields an algorithm for k-coloring semirandom k-colorable graphs, and for the latter algorithm a similar result concerning its running time holds, as also for the independent set algorithm. The results on both problems are essentially best-possible, by the hardness results obtained in .
KeywordsPolynomial Time Algorithm Input Graph Hardness Result Coin Toss Expected Running Time
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