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arXiv · 1511.05109

Minimum Eccentricity Shortest Paths in some Structured Graph Classes

Feodor F. Dragan·Arne Leitert
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Abstract

We investigate the Minimum Eccentricity Shortest Path problem in some structured graph classes. It asks for a given graph to find a shortest path with minimum eccentricity. Although it is NP-hard in general graphs, we demonstrate that a minimum eccentricity shortest path can be found in linear time for distance-hereditary graphs (generalizing the previous result for trees) and give a generalised approach which allows to solve the problem in polynomial time for other graph classes. This includes chordal graphs, dually chordal graphs, graphs with bounded tree-length, and graphs with bounded hyperbolicity. Additionally, we give a simple algorithm to compute an additive approximation for graphs with bounded tree-length and graphs with bounded hyperbolicity.

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Feodor F. Dragan, Arne Leitert. 2015-11-16. Minimum Eccentricity Shortest Paths in some Structured Graph Classes. https://arxiv.org/abs/1511.05109

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