Approximation algorithms for the weighted independent set problem

Authors:
Akihisa Kako;Takao Ono;Tomio Hirata;Magnús M. Halldórsson
Affiliations:
Graduate School of Information Science, nagoya University, nagoya, Japan;Graduate School of Information Science, nagoya University, nagoya, Japan;Graduate School of Information Science, nagoya University, nagoya, Japan;Department of Computer Science, University of Iceland, Reykjavik, Iceland
Venue:
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Year:
2005

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Abstract

In the unweighted case, approximation ratio for the independent set problem has been analyzed in terms of the graph parameters such as the number of vertices, maximum degree, and average degree. In the weighted case, no corresponding results are possible for average degree, since inserting the vertices with small weight decreases the average degree arbitrarily without significantly changing the approximation ratio. In this paper, we introduce weighted measures, namely “weighted” average degree and “weighted” inductiveness, and analyze algorithms for the weighted independent set problem in terms of these parameters.