A reduction algorithm for the weighted stable set problem in claw-free graphs

Authors:
Paolo Nobili;Antonio Sassano
Affiliations:
-;-
Venue:
Discrete Applied Mathematics
Year:
2014

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Abstract

In this article the Lovasz-Plummer clique reduction is extended to the weighted case and used to find a maximum weight stable set in a claw-free graph G with n nodes in O(n^2(n^2+L(n))) time, where L(n) is the complexity of finding a maximum weight augmenting path in a line graph H with n nodes. The best algorithm known to date to solve the latter problem is Gabow's maximum weight matching algorithm (applied to the root graph of H) which has a complexity of O(n^2logn). It follows that our algorithm can produce a maximum weight stable set in a claw-free graph in O(n^4logn) time.