On Partial Vertex Cover and Budgeted Maximum Coverage Problems in Bipartite Graphs

Bugra Caskurlu,K Subramani,Vahan Mkrtchyan,Ojas Parekh

doi:10.1007/978-3-662-44602-7_2

Bugra Caskurlu, K Subramani + Show 2 more

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https://doi.org/10.1007/978-3-662-44602-7_2

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Publication Date: Jan 1, 2014
Citations: 27	License type: cc-by

Affiliation: West Virginia University, Sandia National Laboratories

Abstract

AbstractGraphs are often used to model risk management in various systems. Particularly, Caskurlu et al. in [6] have considered a system which essentially represents a tripartite graph. The goal in this model is to reduce the risk in the system below a predefined risk threshold level. It can be shown that the main goal in this risk management system can be formulated as a Partial Vertex Cover problem on bipartite graphs. It is well-known that the vertex cover problem is in P on bipartite graphs; however, the computational complexity of the partial vertex cover problem on bipartite graphs is open. In this paper, we show that the partial vertex cover problem is NP-hard on bipartite graphs. Then, we show that the budgeted maximum coverage problem (a problem related to partial vertex cover problem) admits an \(\frac{8}{9}\)-approximation algorithm in the class of bipartite graphs, which matches the integrality gap of a natural LP relaxation.KeywordsBipartite graphvertex cover problempartial vertex cover problembudgeted maximum coverage problem

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