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Hardness and approximation for L-EPG and B1-EPG graphs

Epstein, D and Golumbic, MC and Lahiri, A and Morgenstern, G (2020) Hardness and approximation for L-EPG and B1-EPG graphs. In: Discrete Applied Mathematics, 281 . pp. 224-228.

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Official URL: https://doi.org/10.1016/j.dam.2019.10.004


The edge intersection graphs of paths on a grid (or EPG graphs) are graphs whose vertices can be represented as simple paths on a rectangular grid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. We consider the case of single-bend paths and its subclass of ⌞-shaped paths, namely, the classes known as B1-EPG and ⌞-EPG graphs, respectively. We show that fully-subdivided graphs are ⌞-EPG graphs, and later use this result in order to show that the following problems are APX-hard on ⌞-EPG graphs: MINIMUM VERTEX COVER, MAXIMUM INDEPENDENT SET, and MAXIMUM WEIGHTED INDEPENDENT SET, and also that MINIMUM DOMINATING SET is NP-complete on ⌞-EPG graphs. We also observe that MINIMUM COLORING is NP-complete already on ⌞-EPG, which follows from a proof for B1-EPG in Epstein et al. (2013). Finally, we provide efficient constant-factor-approximation algorithms for each of these problems on B1-EPG graphs.

Item Type: Journal Article
Publication: Discrete Applied Mathematics
Publisher: Elsevier B.V.
Additional Information: The copyright for this article belongs to Elsevier B.V.
Keywords: Approximation algorithms; Graph algorithms; Graph structures; Graphic methods, B1-EPG graphs; Constant-factor approximation algorithms; Intersection graph; Maximum independent sets; Maximum weighted independent set; Minimum dominating set; Paths on a grid; Subdivided graphs, Graph theory
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 03 Feb 2023 05:08
Last Modified: 03 Feb 2023 05:08
URI: https://eprints.iisc.ac.in/id/eprint/79827

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