Chakraborty, Dibyayan ;
Dailly, Antoine ;
Das, Sandip ;
Foucaud, Florent ;
Gahlawat, Harmender ;
Ghosh, Subir Kumar
Complexity and Algorithms for ISOMETRIC PATH COVER on Chordal Graphs and Beyond
Abstract
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 minimumsize set of isometric paths. Although this problem has been considered from a structural point of view (in particular, regarding applications to pursuitevasion games), it is little studied from the algorithmic perspective. We consider Isometric Path Cover on chordal graphs, and show that the problem is NPhard for this class. On the positive side, for chordal graphs, we design a 4approximation 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 kchordal 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.
BibTeX  Entry
@InProceedings{chakraborty_et_al:LIPIcs.ISAAC.2022.12,
author = {Chakraborty, Dibyayan and Dailly, Antoine and Das, Sandip and Foucaud, Florent and Gahlawat, Harmender and Ghosh, Subir Kumar},
title = {{Complexity and Algorithms for ISOMETRIC PATH COVER on Chordal Graphs and Beyond}},
booktitle = {33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
pages = {12:112:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959772587},
ISSN = {18688969},
year = {2022},
volume = {248},
editor = {Bae, Sang Won and Park, Heejin},
publisher = {Schloss Dagstuhl  LeibnizZentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/17297},
URN = {urn:nbn:de:0030drops172974},
doi = {10.4230/LIPIcs.ISAAC.2022.12},
annote = {Keywords: Shortest paths, Isometric path cover, Chordal graph, Interval graph, ATfree graph, Approximation algorithm, FPT algorithm, Treewidth, Chordality, Treelength}
}
14.12.2022
Keywords: 

Shortest paths, Isometric path cover, Chordal graph, Interval graph, ATfree graph, Approximation algorithm, FPT algorithm, Treewidth, Chordality, Treelength 
Seminar: 

33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Issue date: 

2022 
Date of publication: 

14.12.2022 