Minimum Eccentricity Shortest Path Problem with Respect to Structural Parameters
Martin Ku\v{c}era, Ond\v{r}ej Such\'y
TL;DR
This paper introduces fixed-parameter tractable algorithms for the NP-complete Minimum Eccentricity Shortest Path Problem, leveraging structural graph parameters such as modular width and treewidth.
Contribution
The paper develops new fixed-parameter algorithms for the problem based on various structural graph parameters, advancing the understanding of its computational complexity.
Findings
FPT algorithms parameterized by modular width and distance to cluster graph.
FPT algorithms combining treewidth with eccentricity.
FPT algorithms based on maximum leaf number.
Abstract
The Minimum Eccentricity Shortest Path Problem consists in finding a shortest path with minimum eccentricity in a given undirected graph. The problem is known to be NP-complete and W[2]-hard with respect to the desired eccentricity. We present fpt-algorithms for the problem parameterized by the modular width, distance to cluster graph, the combination of treewidth with the desired eccentricity, and maximum leaf number.
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