Improved Upper Bounds for Partial Vertex Cover
The Partial Vertex Cover problem is to decide whether a graph contains at most k nodes covering at least t edges. We present deterministic and randomized algorithms with run times of O *(1.396 t ) and O *(1.2993 t ), respectively. For graphs of maximum degree three, we show how to solve this problem in O *(1.26 t ) steps. Finally, we give an O *(3 t ) algorithm for Exact Partial Vertex Cover, which asks for at most k nodes covering exactly t edges.
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- 2.Bar-Yehuda, R.: Using homogenous weights for approximating the partial cover problem. In: Proc. of 10th SODA, pp. 71–75 (1999)Google Scholar
- 4.Bshouty, N.H., Burroughs, L.: Massaging a linear programming solution to give a 2-approximation for a generalization of the vertex cover problem. In: Meinel, C., Morvan, M. (eds.) STACS 1998. LNCS, vol. 1373, pp. 298–308. Springer, Heidelberg (1998)Google Scholar
- 6.Chen, J., Kanj, I.A., Xia, G.: Simplicity is beauty: Improved upper bounds for vertex cover. Technical Report TR05-008, School of CTI, DePaul University (2005)Google Scholar
- 8.Fomin, F., Grandoni, F., Kratsch, D.: A measure & conquer approach for the analysis of exact algorithms. Technical Report 359, Department of Informatics, University of Bergen (July 2007)Google Scholar
- 18.Robson, J.M.: Finding a maximum independent set in time O(2n/4). Technical Report 1251-01, Université Bordeaux I, LaBRI (2001)Google Scholar