TY - GEN

T1 - Vertex cover gets faster and harder on low degree graphs

AU - Agrawal, Akanksha

AU - Govindarajan, Sathish

AU - Misra, Neeldhara

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=84904733131&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-08783-2_16

DO - 10.1007/978-3-319-08783-2_16

M3 - Conference contribution

AN - SCOPUS:84904733131

SN - 9783319087825

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 179

EP - 190

BT - Computing and Combinatorics - 20th International Conference, COCOON 2014, Proceedings

PB - Springer Verlag

T2 - 20th International Computing and Combinatorics Conference, COCOON 2014

Y2 - 4 August 2014 through 6 August 2014

ER -