Hardness Results and an Exact Exponential Algorithm for the Spanning Tree Congestion Problem

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 (exponentialtime) exact algorithm that runs in O∗(2n) time, where n denotes the number of vertices. Additionally, we present simple combinatorial lemmas, which yield a constant-factor approximation algorithm for cographs, and a linear-time algorithm for chordal cographs. Submitted: May 2011 Reviewed: September 2011 Revised: October 2011 Accepted: October 2011 Final: October 2011 Published: October 2011 Article type: Regular paper Communicated by: S.-H. Hong Extended abstract of this paper appeared in the proceedings of TAMC 2011 [22]. E-mail addresses: [email protected] (Yoshio Okamoto) [email protected] (Yota Otachi) [email protected] (Ryuhei Uehara) [email protected] (Takeaki Uno) 728 Okamoto et al. Spanning Tree Congestion Problem