Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arya, V., et al.: Local Search Heuristics for k-median and Facility Location Problems. In: The proceedings of STOC, pp. 21–29 (2001)
Arkin, E.M., Hassin, R., Levin, A.: Approximation for Minimum and Min-Max Vehicle Routing Problems. Journal of Algorithms 59, 1–18 (2006)
Desrochers, M., Desrosiers, J., Solomon, M.: A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows. Operation Research 40, 342–354 (1992)
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)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. W.H. Freeman, San Francisco (1979)
Kohen, A., Kan, A.R., Trienekens, H.: Vehicle Routing with Time Windows. Operations Research 36, 266–273 (1987)
Nagarajan, V., Ravi, R.: Minimum vehicle routing with a common deadline. In: Díaz, J., et al. (eds.) APPROX 2006 and RANDOM 2006. LNCS, vol. 4110, Springer, Heidelberg (2006)
Savelsbergh, M.: Local Search for Routing Problems with Time Windows. Annals of Operations Research 4, 285–305 (1985)
Tan, K.C., et al.: Heuristic Methods for Vehicle Routing Problems with Time Windows. Artificial Intelligence in Engineering, 281–295 (2001)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhao, W., Zhang, P. (2007). Approximation to the Minimum Rooted Star Cover Problem. In: Cai, JY., Cooper, S.B., Zhu, H. (eds) Theory and Applications of Models of Computation. TAMC 2007. Lecture Notes in Computer Science, vol 4484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72504-6_61
Download citation
DOI: https://doi.org/10.1007/978-3-540-72504-6_61
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72503-9
Online ISBN: 978-3-540-72504-6
eBook Packages: Computer ScienceComputer Science (R0)