Abstract
Given a ring of size n and a set K of traffic demands, the ring loading problem with demand splitting (RLPW) is to determine a routing to minimize the maximum load on the edges. In the problem, a demand between two nodes can be split into two flows and then be routed along the ring in different directions. If the two flows obtained by splitting a demand are restricted to integers, this restricted version is called the ring loading problem with integer demand splitting (RLPWI). In this paper, efficient algorithms are proposed for the RLPW and the RLPWI. Both the proposed algorithms require O(|K|+t s ) time, where t s is the time for sorting |K| nodes. If |K| ≥ n ε for some small constant ε> 0, integer sort can be applied and thus t s =O(|K|); otherwise, t s = O(|K|log|K|). The proposed algorithms improve the previous upper bounds from O(n|K|) for both problems.
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
Amico, M.D., Labbe, M., Maffioli, F.: Exact solution of the SONET ring loading problem. Operations Research Letters 25, 119–129 (1999)
Cosares, S., Saniee, I.: An optimal problem related to balancing loads on SONET rings. Telecommunication Systems 3, 165–181 (1994)
Gabow, H.N., Tarjan, R.E.: A linear-time algorithm for a special case of disjoint set union. Journal of Computer and System Sciences 30, 209–221 (1985)
Lee, C.Y., Chang, S.G.: Balancing loads on SONET rings with integer demand splitting. Computers Operations Research 24, 221–229 (1997)
Myung, Y.-S., Kim, H.-G., Tcha, D.-W.: Optimal load balancing on SONET bidirectional rings. Operations Research 45, 148–152 (1997)
Myung, Y.-S.: An efficient algorithm for the ring loading problem with integer demand splitting. SIAM Journal on Discrete Mathematics 14(3), 291–298 (2001)
Schrijver, A., Seymour, P., Winkler, P.: The ring loading problem. SIAM Journal on Discrete Mathematics 11, 1–14 (1998)
Vachani, R., Shulman, A., Kubat, P.: Multi-commodity flows in ring networks. INFORMS Journal on Computing 8, 235–242 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, BF., Hsieh, YH., Yeh, LP. (2003). Efficient Algorithms for the Ring Loading Problem with Demand Splitting. In: Di Battista, G., Zwick, U. (eds) Algorithms - ESA 2003. ESA 2003. Lecture Notes in Computer Science, vol 2832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39658-1_47
Download citation
DOI: https://doi.org/10.1007/978-3-540-39658-1_47
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20064-2
Online ISBN: 978-3-540-39658-1
eBook Packages: Springer Book Archive