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Vertex Cover Gets Faster and Harder on Low Degree Graphs

Agrawal, Akanksha and Govindarajan, Sathish and Misra, Neeldhara (2014) Vertex Cover Gets Faster and Harder on Low Degree Graphs. In: 20th International Conference on Computing and Combinatorics (COCOON), AUG 04-06, 2014, Atlanta, GA, pp. 179-190.

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Official URL: http://arxiv.org/abs/1404.5566

Abstract

The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric objects, often turns out to be exactly the vertex cover problem on restricted classes of graphs. In this work we explore a particular instance of such a phenomenon. We consider the problem of hitting all axis-parallel slabs induced by a point set P, and show that it is equivalent to the problem of finding a vertex cover on a graph whose edge set is the union of two Hamiltonian Paths. We show the latter problem to be NP-complete, and also give an algorithm to find a vertex cover of size at most k, on graphs of maximum degree four, whose running time is 1.2637(k) n(O(1)).

Item Type: Conference Proceedings
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Additional Information: Copy right for this article belongs to the SPRINGER-VERLAG BERLIN, HEIDELBERGER PLATZ 3, D-14197 BERLIN, GERMANY
Department/Centre: Division of Electrical Sciences > Computer Science & Automation (Formerly, School of Automation)
Date Deposited: 04 Dec 2014 04:49
Last Modified: 04 Dec 2014 04:49
URI: http://eprints.iisc.ernet.in/id/eprint/50375

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