2026-07-23T20:16:42Z https://drops.dagstuhl.de/oai
oai:drops-oai.dagstuhl.de:17297 2024-03-06T10:59:23Z ddc:004 open_access
Complexity and Algorithms for ISOMETRIC PATH COVER on Chordal Graphs and Beyond Chakraborty, Dibyayan Dailly, Antoine Das, Sandip Foucaud, Florent Gahlawat, Harmender Ghosh, Subir Kumar Shortest paths Isometric path cover Chordal graph Interval graph AT-free graph Approximation algorithm FPT algorithm Treewidth Chordality Treelength A path is isometric if it is a shortest path between its endpoints. In this article, we consider the graph covering problem Isometric Path Cover, where we want to cover all the vertices of the graph using a minimum-size set of isometric paths. Although this problem has been considered from a structural point of view (in particular, regarding applications to pursuit-evasion games), it is little studied from the algorithmic perspective. We consider Isometric Path Cover on chordal graphs, and show that the problem is NP-hard for this class. On the positive side, for chordal graphs, we design a 4-approximation algorithm and an FPT algorithm for the parameter solution size. The approximation algorithm is based on a reduction to the classic path covering problem on a suitable directed acyclic graph obtained from a breadth first search traversal of the graph. The approximation ratio of our algorithm is 3 for interval graphs and 2 for proper interval graphs. Moreover, we extend the analysis of our approximation algorithm to k-chordal graphs (graphs whose induced cycles have length at most k) by showing that it has an approximation ratio of k+7 for such graphs, and to graphs of treelength at most 𝓁, where the approximation ratio is at most 6𝓁+2. Schloss Dagstuhl – Leibniz-Zentrum fΓΌr Informatik Dibyayan Chakraborty and Antoine Dailly and Sandip Das and Florent Foucaud and Harmender Gahlawat and Subir Kumar Ghosh 2022 Is Part Of LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2022.12 urn:nbn:de:0030-drops-172974 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.12 eng https://creativecommons.org/licenses/by/4.0/legalcode