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

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 ℓ and have exactly one endpoint on ℓ. 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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A graph G with n vertices is called an outerstring graph if it has an in...
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• ### Exact recovery of Planted Cliques in Semi-random graphs

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• ### Assembling Omnitigs using Hidden-Order de Bruijn Graphs

De novo DNA assembly is a fundamental task in Bioinformatics, and findin...
05/14/2018 ∙ by Diego Díaz-Domínguez, et al. ∙ 0