## Complexity Results for the Spanning Tree Congestion Problem (2010)

Citations: | 1 - 1 self |

### BibTeX

@MISC{Otachi10complexityresults,

author = {Yota Otachi and Hans L. Bodlaender and Erik Jan Van Leeuwen},

title = {Complexity Results for the Spanning Tree Congestion Problem },

year = {2010}

}

### OpenURL

### Abstract

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.