A note on greedy algorithms for the maximum weighted independent set problem

Authors:
Shuichi Sakai;Mitsunori Togasaki;Koichi Yamazaki
Affiliations:
Department of Computer Science, Gunma University, 1-5-1 Tenjin-cho, Kiryu zip:376-8515 Gunma, Japan;Department of Computer Science, Gunma University, 1-5-1 Tenjin-cho, Kiryu zip:376-8515 Gunma, Japan;Department of Computer Science, Gunma University, 1-5-1 Tenjin-cho, Kiryu zip:376-8515 Gunma, Japan
Venue:
Discrete Applied Mathematics
Year:
2003

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Abstract

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.