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arXiv · 2107.05198

Finding a Maximum Clique in a Grounded 1-Bend String Graph

J. Mark Keil·Debajyoti Mondal·Ehsan Moradi·Yakov Nekrich
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Abstract

A grounded 1-bend string graph is an intersection graph of a set of polygonal lines, each with one bend, such that the lines lie above a common horizontal line $\ell$ and have exactly one endpoint on $\ell$. We show that the problem of finding a maximum clique in a grounded 1-bend string graph is APX-hard, even for strictly $y$-monotone strings. For general 1-bend strings, the problem remains APX-hard even if we restrict the position of the bends and end-points to lie on at most three parallel horizontal lines. We give fast algorithms to compute a maximum clique for different subclasses of grounded segment graphs, which are formed by restricting the strings to various forms of $L$-shapes.

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J. Mark Keil, Debajyoti Mondal, Ehsan Moradi, Yakov Nekrich. 2021-07-12. Finding a Maximum Clique in a Grounded 1-Bend String Graph. https://arxiv.org/abs/2107.05198

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