Parameterized Complexity of the Spanning Tree Congestion Problem
Algorithmica(2011)
摘要
We study the problem of determining the spanning tree congestion of a graph. We present some sharp contrasts in the parameterized complexity of this problem. First, we show that on apex-minor-free graphs, a general class of graphs containing planar graphs, graphs of bounded treewidth, and graphs of bounded genus, the problem to determine whether a given graph has spanning tree congestion at most k can be solved in linear time for every fixed k . We also show that for every fixed k and d the problem is solvable 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 ≥8. Moreover, the hardness result holds for graphs excluding the complete graph on 6 vertices as a minor. We also observe that for k ≤3 the problem becomes polynomially time solvable.
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关键词
Spanning tree congestion,Graph minor,Parameterized algorithms,Apex graph
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