Parameterized Complexity of 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 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...

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Bibliographic Details
Published in:	Algorithmica Vol. 64; no. 1; pp. 85 - 111
Main Authors:	Bodlaender, Hans L., Fomin, Fedor V., Golovach, Petr A., Otachi, Yota, van Leeuwen, Erik Jan
Format:	Journal Article
Language:	English
Published:	New York Springer-Verlag 01.09.2012
Subjects:	Algorithm Analysis and Problem Complexity Algorithms Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Mathematics of Computing Theory of Computation Parameterized algorithms Graph minor Apex graph Spanning tree congestion
ISSN:	0178-4617, 1432-0541
Online Access:	Get full text
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Summary:	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.
ISSN:	0178-4617 1432-0541
DOI:	10.1007/s00453-011-9565-7