• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.4
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• pp.99-108
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• 2001

In the ring loading problem with demand splitting, traffic demands are given for each pall of nodes in an undirected ring network and a flow is routed in either of the two directions, clockwise and counter-clockwise. The load of a link is the sum of the flows routed through the link and the objective of the problem is to minimize the maximum load on the ring. The fastest a1gorithm to date is Myung, Kim and Tcha＇s a1gorithm that runs in Ο(n｜K｜) time where n is the number of nodes and K is the index set of the origin-destination pairs of nodes having flow traffic demands. Here we develop an a1gorithm for the ring loading problem with demand splitting that improves the rerouting step of Myung, Kim and Tcha＇s a1gorithm arid runs in Ο(min{n｜K｜, n$^2$}) time.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.3
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• pp.49-62
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• 1998

In the ring loading problem, traffic demands are given for each pair of nodes in an undirected ring network with n nodes and a flow is routed in either of the two directions, clockwise and counter-clockwise. The load of a link is the sum of the flows routed through the link and the objective of the Problem is to minimize the maximum load on the ring. In the ring loading problem with integer demand splitting, each demand can be split between the two directions and the flow routed in each direction is restricted to integers. Recently, Vachani et al. ［INFORMS J. Computing 8 (1996) 235-242］ have developed an Ο(n$^3$) algorithm for solving this integer version of the ring loading problem and independently, Schrijver et al. ［to appear in SIAM J. Disc. Math.］ have presented an algorithm which solves the problem with ｛0,1｝ demands in Ο（n$^2$｜K｜ ) time where K denotes the index set of the origin-desㅇtination pairs of nodes having flow demands. In this paper, we develop an algorithm which solves the problem in Ο(n ｜K｜) time.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.05a
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• pp.306-310
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• 2004

In this paper, we consider the Ring Loading Problem with integer demand splitting (RLP). The problem is given with a ring network, in which a required traffic requirement between each selected node pair must be routed on it. Each traffic requirement can be routed in both directions on the ring network while splitting each traffic requirement in two directions only by integer is allowed. The problem is to find an optimal routing of each traffic requirement which minimizes the capacity requirement. Here, the capacity requirement is defined as the maximum of traffic loads imposed on each link on the network. We formulate the problem as an integer program. By characterizing every extreme point solution to the LP relaxation of the formulation, we show that the optimal objective value of the LP relaxation is equal to p or p+0.5, where p is a nonnegative integer. We also show that the difference between the optimal objective value of RLP and that of the LP relaxation is at most 1. Therefore, we can verify that the optimal objective value of RLP is p+1 if that of the LP relaxation is p+0.5. On the other hand, we present a strengthened LP with size polynomially bounded by the input size, which provides enough information to determine if the optimal objective value of RLP is p or p+1.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.10a
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• pp.125-128
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• 1996

In this paper, we consider a ring loading problem, which arises in the design of SONET bidirectional rings. We deal with the case where demands are allowed to be split and routed in two different directions. Even if integral . demands are given, the optimal solution of the problem doesn't always have integral values. We present an efficient algorithm which produces an integral optimal solution.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1997.10a
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• pp.51-51
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• 1997