寻找大型独立集的启发式方法,并应用于半随机图的着色

U. Feige, J. Kilian
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引用次数: 34

摘要

研究了一种寻找独立集的半随机图模型。对于/spl alpha/>0,通过混合随机决策和对抗决策,构造了一个独立集S为site /spl alpha/n的n顶点图。随机独立的,概率为p,每对顶点,一个在S内,另一个不在S内,由一条边连接。然后对手可以任意添加边(假设S仍然是一个独立的集合)。p越小,对手对半随机图的控制就越大。当p>(1+/spl epsiv/)ln n/|S|时,对于任意常数/spl epsiv/>0,我们设计了高概率恢复S的启发式算法。我们证明了当p<(1-/spl subsiv /) In n/|S|时,除非NP/spl subv /BPP,否则无法恢复大小为|S|的独立集。我们利用我们的研究成果获得了A. Blum和J. Spencer(1995)引入的k-可着色半随机图模型的大大改进的着色算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Heuristics for finding large independent sets, with applications to coloring semi-random graphs
We study a semi-random graph model for finding independent sets. For /spl alpha/>0, an n-vertex graph with an independent set S of site /spl alpha/n is constructed by blending random and adversarial decisions. Randomly and independently with probability p, each pair of vertices, such that one is in S and the other is not, is connected by an edge. An adversary can then add edges arbitrarily (provided that S remains an independent set). The smaller p is, the larger the control the adversary has over the semi-random graph. We design heuristics that with high probability recover S when p>(1+/spl epsiv/)ln n/|S|, for any constant /spl epsiv/>0. We show that when p<(1-/spl epsiv/) In n/|S|, an independent set of size |S| cannot be recovered, unless NP/spl sube/BPP. We use our remits to obtain greatly improved coloring algorithms for the model of k-colorable semi-random graphs introduced by A. Blum and J. Spencer (1995).
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