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: (i) 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; (ii) 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; (iii) there is an efficient 2-approximation algorithm for computing the path-length of an arbitrary graph; (iv) AT-free graphs and some intersection families of graphs have path-length at most 2; (v) 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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Dragan, F.F., Köhler, E., Leitert, A. (2014). Line-Distortion, Bandwidth and Path-Length of a Graph. In: Ravi, R., Gørtz, I.L. (eds) Algorithm Theory – SWAT 2014. SWAT 2014. Lecture Notes in Computer Science, vol 8503. Springer, Cham. https://doi.org/10.1007/978-3-319-08404-6_14
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DOI: https://doi.org/10.1007/978-3-319-08404-6_14
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