Graphs 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 8/9-approximation algorithm in the class of bipartite graphs, which matches the integrality gap of a natural LP relaxation. © 2014 IFIP International Federation for Information Processing.
CITATION STYLE
Caskurlu, B., Mkrtchyan, V., Parekh, O., & Subramani, K. (2014). On partial vertex cover and budgeted maximum coverage problems in bipartite graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8705 LNCS, pp. 13–26). Springer Verlag. https://doi.org/10.1007/978-3-662-44602-7_2
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