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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Vydané v:Algorithmica Ročník 64; číslo 1; s. 85 - 111
Hlavní autori: Bodlaender, Hans L., Fomin, Fedor V., Golovach, Petr A., Otachi, Yota, van Leeuwen, Erik Jan
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer-Verlag 01.09.2012
Predmet:
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
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Popis
Shrnutí: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