2014 Second International Symposium on Computing and Networking (CANDAR) (2014)

Shizuoka, Japan

Dec. 10, 2014 to Dec. 12, 2014

ISBN: 978-1-4799-4152-0

pp: 68-75

ABSTRACT

In this paper, we consider a new variant of the minimum weight vertex cover problem (MWVC) in which each vertex can cover a fractional amount of edges incident on it. For example, if the degree of a vertex is five and the designated fraction is 2/3, then it can cover at most ? (2/3) × 5 ? = 4 edges among five incident edges. This problem is motivated by a sustainable monitoring of the environment by a set of agents placed at the vertices of graph G so that the failure of agents can be easily recovered by its nearby agents within a short time. This paper investigates the computational complexity of this optimization problem. More specifically, we show that the number of vertices of odd degree, denoted as no, plays a key role in determining the hardness of the problem, so that when the given fraction is 1/2, the complexity of the problem increases as no increases, i.e., It can be solved in polynomial time when no = O (1), although it cannot be approximated within an arbitrary constant factor when no = n, where n is the total number of vertices in the given graph.

INDEX TERMS

Polynomials, Approximation methods, Joining processes, Monitoring, Computational complexity, Approximation algorithms, Optimization

CITATION

S. Fujita, "On Vertex Cover with Fractional Fan-Out Bound,"

*2014 Second International Symposium on Computing and Networking (CANDAR)*, Shizuoka, Japan, 2014, pp. 68-75.

doi:10.1109/CANDAR.2014.10

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