Journal of Combinatorial Optimization

, Volume 10, Issue 2, pp 99–111 | Cite as

Maximizing Profits of Routing in WDM Networks

  • Jianping Li
  • Kang Li
  • Lusheng Wang
  • Hao Zhao


Let G = (V, E) be a ring (or chain) network representing an optical wavelength division multiplexing (WDM) network with k channels, where each edge e j has an integer capacity c j . A request s i ,t i is a pair of two nodes in G. Given m requests s i ,t i , i = 1, 2, ..., m, each with a profit value p i , we would like to design/route a k-colorable set of paths for some (may not be all) of the m requests such that each edge e j in G is used at most c j times and the total profit of the set of designed paths is maximized. Here two paths cannot have the same color (channel) if they share some common edge(s).

This problem arises in optical communication networks. In this paper, we present a polynomial-time algorithm to solve the problem when G is a chain. When G is a ring, however, the optimization problem is NP-hard (Wan and Liu, 1998), we present a 2-approximation algorithm based on our solution to the chain network. Similarly, some results in a bidirected chain and a bidirected ring are obtained.


minimum-cost flow routing path coloring approximation algorithm 


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of MathematicsYunnan UniversityKunmingP.R. China
  2. 2.School of Information Science and EngineeringShandong UniversityJinanP.R. China
  3. 3.Department of Computer ScienceCity University of Hong KongKowloon, Hong KongP.R. China

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