Line-distortion, Bandwidth and Path-length of a graph

Feodor F. Dragan; Ekkehard Köhler; Arne Leitert

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arXiv · 1409.8389

Line-distortion, Bandwidth and Path-length of a graph

Feodor F. Dragan·Ekkehard Köhler·Arne Leitert

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Abstract

We investigate the minimum line-distortion and the minimum bandwidth problems on unweighted graphs and their relations with the minimum length of a Robertson-Seymour's path-decomposition. The length of a path-decomposition of a graph is the largest diameter of a bag in the decomposition. The path-length of a graph is the minimum length over all its path-decompositions. In particular, we show: - if a graph $G$ can be embedded into the line with distortion $k$, then $G$ admits a Robertson-Seymour's path-decomposition with bags of diameter at most $k$ in $G$; - for every class of graphs with path-length bounded by a constant, there exist an efficient constant-factor approximation algorithm for the minimum line-distortion problem and an efficient constant-factor approximation algorithm for the minimum bandwidth problem; - there is an efficient 2-approximation algorithm for computing the path-length of an arbitrary graph; - AT-free graphs and some intersection families of graphs have path-length at most 2; - for AT-free graphs, there exist a linear time 8-approximation algorithm for the minimum line-distortion problem and a linear time 4-approximation algorithm for the minimum bandwidth problem.

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Feodor F. Dragan, Ekkehard Köhler, Arne Leitert. 2014-09-30. Line-distortion, Bandwidth and Path-length of a graph. https://arxiv.org/abs/1409.8389

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