Approximation to the Minimum Rooted Star Cover Problem
In this paper, we study the following minimum rooted star cover problem: given a complete graph G = (V, E) with a length function l: E →ℤ + that satisfies the triangle inequality, a designated root vertex r ∈ V, and a length bound D, the objective is to find a minimum cardinality set of rooted stars, that covers all vertices in V such that the length of each rooted star is at most D, where a rooted star is a subset of E having a common center s ∈ V and containing the edge (r, s). This problem is NP-complete and we present a constant ratio approximation algorithm for this problem.
KeywordsMinimum Rooted Star Cover Approximation Algorithm
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- 1.Arya, V., et al.: Local Search Heuristics for k-median and Facility Location Problems. In: The proceedings of STOC, pp. 21–29 (2001)Google Scholar
- 4.Even, G., et al.: Covering Graph Using Trees and Stars. In: Arora, S., et al. (eds.) RANDOM 2003 and APPROX 2003. LNCS, vol. 2764, pp. 24–25. Springer, Heidelberg (2003)Google Scholar
- 6.Kohen, A., Kan, A.R., Trienekens, H.: Vehicle Routing with Time Windows. Operations Research 36, 266–273 (1987)Google Scholar
- 9.Tan, K.C., et al.: Heuristic Methods for Vehicle Routing Problems with Time Windows. Artificial Intelligence in Engineering, 281–295 (2001)Google Scholar