Approximation algorithms for the weighted independent set problem in sparse graphs

Authors:
Akihisa Kako;Takao Ono;Tomio Hirata;Magnús M. Halldórsson
Affiliations:
School of Information Science, Nagoya University, Nagoya, Japan;School of Information Science, Nagoya University, Nagoya, Japan;School of Information Science, Nagoya University, Nagoya, Japan;School of Computer Science, Reykjavík University, Reykjavík, Iceland
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

The approximability of the unweighted independent set problem has been analyzed in terms of sparseness parameters such as the average degree and inductiveness. In the weighted case, no corresponding results are possible for average degree, since adding vertices of small weight can decrease the average degree arbitrarily without significantly changing the approximation ratio. In this paper, we introduce two weighted measures, namely weighted average degree and weighted inductiveness, and analyze algorithms for the weighted independent set problem in terms of these parameters.