Abstract
We study the directed ring loading problem with penalty cost, which is to select some of given multicast requests represented by hyperedges with different demands and embed them in a directed ring, such that the sum of the maximum congestion among all links on the ring and the total penalty cost of the unselected multicast requests is minimized. We prove that this problem is NP-hard even if the demand is divisible, and then design a 1.582-approximation algorithm for the demand divisible case and a 3-approximation algorithm for the demand indivisible case, respectively. As a consequence, for any ε > 0, we present a (1.582 + ε)-approximation algorithm for the case where every multicast request contains exactly one sink.
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References
Becchetti, L., Ianni, M.D., Spaccamela, A.M.: Approximation algorithms for routing and call scheduling in all-optical chains and rings. Theoretical Computer Science 287(2), 429–448 (2002)
Frank, A., Nishizeki, T., Saito, N., Suzuki, H., Tardos, E.: Algorithms for routing around a rectangle. Discrete Applied Mathematics 40(3), 363–378 (1992)
Ganley, J.L., Cohoon, J.P.: Minimum-congestion hypergraph embedding in a cycle. IEEE Transactions on Computers 46(5), 600–602 (1997)
Garey, M.R., Johnson, D.S.: Computer and Intractability: A Guide to The Theory of NP-Completeness. W. H. Freeman and Company, San Francisco (1979)
Gonzalez, T.: Improved approximation algorithm for embedding hyperedges in a cycle. Information Processing Letters 67(5), 267–271 (1998)
Gu, Q., Wang, Y.: Efficient algorithms for minimum congestion hypergraph embedding in a cycle. IEEE Transactions on Parallel and Distributed Systems 17(3), 205–214 (2006)
Ho, H., Lee, S.: Improved approximation algorithms for weighted hypergraph embedding in a cycle. SIAM Journal on Optimization 18(4), 1490–1500 (2008)
Lee, S., Ho, H.: On minimizing the maximum congestion for weighted hypergraph embedding in a cycle. Information Processing Letters 87(5), 271–275 (2003)
Li, G., Deng, X., Xu, Y.: A polynomial time approximation scheme for embedding hypergraph in a cycle. ACM Transactions on Algorithms 5(2), Article No 20 (2009)
Li, J., Li, W., Wang, L.: A polynomial time approximation scheme for embedding a directed hypergraph on a weighted ring. Journal of Combinatorial Optimization 24(3), 319–328 (2012)
Li, K., Wang, L.: A polynomial time approximation scheme for embedding a directed hypergraph on a ring. Information Processing Letters 97(5), 203–207 (2006)
Li, W., Li, J., Guan, L.: Approximation algorithms for the ring loading problem with penalty cost. Information Processing Letters 114(1-2), 56–59 (2014)
Schrijver, A., Seymour, P., Winkler, P.: The ring loading problem. SIAM Review 41, 777–791 (1999)
Wang, Q., Liu, X., Zheng, X., Zhao, X.: A 2-approximation algorithm for weighted directed hypergraph embedding in a cycle. In: The 4th International Conference on Natural Computation, pp. 377–381 (2008)
Wilfong, G., Winkler, P.: Ring routing and wavelength translation. In: Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 333–341 (1998)
Yang, C., Li, G.: A polynomial time approximation scheme for embedding hypergraph in a weighted cycle. Theoretical Computer Science 412(48), 6786–6793 (2011)
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Guan, L., Li, J., Zhang, X., Li, W. (2015). The Directed Ring Loading with Penalty Cost. In: Rahman, M.S., Tomita, E. (eds) WALCOM: Algorithms and Computation. WALCOM 2015. Lecture Notes in Computer Science, vol 8973. Springer, Cham. https://doi.org/10.1007/978-3-319-15612-5_3
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DOI: https://doi.org/10.1007/978-3-319-15612-5_3
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