Hardness results and an exact exponential algorithm for the spanning tree congestion problem

Authors:
Yoshio Okamoto;Yota Otachi;Ryuhei Uehara;Takeaki Uno
Affiliations:
Center for Graduate Education Initiative, JAIST, Asahidai, Nomi, Ishikawa, Japan;Graduate School of Information Sciences, Tohoku University, Sendai, Japan;School of Information Science, JAIST, Asahidai, Nomi, Ishikawa, Japan;National Institute of Informatics, Hitotsubashi, Chiyoda-ku, Tokyo, Japan
Venue:
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Year:
2011

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Abstract

Spanning tree congestion is a relatively new graph parameter, which has been studied intensively. This paper studies the complexity of the problem to determine the spanning tree congestion for non-sparse graph classes, while it was investigated for some sparse graph classes before. We prove that the problem is NP-hard even for chain graphs and split graphs. To cope with the hardness of the problem, we present a fast (exponential-time) exact algorithm that runs in O*(2n) time, where n denotes the number of vertices. Additionally, we provide a constant-factor approximation algorithm for cographs, and a linear-time algorithm for chordal cographs.