A note on greedy algorithms for the maximum weighted independent set problem
In this paper, we consider three simple and natural greedy algorithms for the maximum weighted independent set problem. We show that two of them output an independent set of weight at least Σv∈V(G) W(v)/[d(v) + 1] and the third algorithm outputs an independent set of weight at least Σv∈V(G) W(v)2/[Σu∈NG+(v) W(u)].These results are generalization of theorem of Caro and Wei.
Journal of Graph Algorithms and Applications Approximations of Weighted Independent Set and Hereditary Subset Problems
The focus of this study is to clarify the approximability of the important versions of the maximum independent set problem, and to apply, where possible, the technique to related hereditary subgraph and subset problem. We report improved performance ratios for the Independent Set problem in weighted general graphs, weighted bounded-degree graphs, and in sparse graphs. Other problems with better than previously reported ratios include Weighted Set Packing, Longest Subsequence, Maximum Independent Sequence, and Independent Set in hypergraphs.
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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