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Chakraborty, Dibyayan [Author]; Dailly, Antoine [Author]; Das, Sandip [Author]; Foucaud, Florent [Author]; Gahlawat, Harmender [Author]; Ghosh, Subir Kumar [Author] ; Dibyayan Chakraborty and Antoine Dailly and Sandip Das and Florent Foucaud and Harmender Gahlawat and Subir Kumar Ghosh [Contributor]

Complexity and Algorithms for ISOMETRIC PATH COVER on Chordal Graphs and Beyond

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  • Media type: Text; E-Article; Electronic Conference Proceeding
  • Title: Complexity and Algorithms for ISOMETRIC PATH COVER on Chordal Graphs and Beyond
  • Contributor: Chakraborty, Dibyayan [Author]; Dailly, Antoine [Author]; Das, Sandip [Author]; Foucaud, Florent [Author]; Gahlawat, Harmender [Author]; Ghosh, Subir Kumar [Author]
  • Published: Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2022
  • Language: English
  • DOI: https://doi.org/10.4230/LIPIcs.ISAAC.2022.12
  • Keywords: Treelength ; Chordality ; Isometric path cover ; Interval graph ; AT-free graph ; Chordal graph ; Treewidth ; Approximation algorithm ; Shortest paths ; FPT algorithm
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  • Description: 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.
  • Access State: Open Access