Complexity Results for the Spanning Tree Congestion Problem
We study the problem of determining the spanning tree congestion of a graph. We present some sharp contrasts in the complexity of this problem. First, we show that for every fixed k and d the problem to determine whether a given graph has spanning tree congestion at most k can be solved in linear time for graphs of degree at most d. In contrast, if we allow only one vertex of unbounded degree, the problem immediately becomes NP-complete for any fixed k ≥ 10. For very small values of k however, the problem becomes polynomially solvable. We also show that it is NP-hard to approximate the spanning tree congestion within a factor better than 11/10. On planar graphs, we prove the problem is NP-hard in general, but solvable in linear time for fixed k.
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- 1.Berman, P., Karpinski, M., Scott, A.D.: Approximation hardness of short symmetric instances of MAX-3SAT, ECCC TR03-049 (2003)Google Scholar
- 23.Raspaud, A., Sýkora, O., Vrťo, I.: Congestion and dilation, similarities and differences: A survey. In: SIROCCO 2000, pp. 269–280. Carleton Scientific (2000)Google Scholar