Approximation algorithms for constructing wavelength routing networks

• Published in: Networks Vol. 40; no. 1; pp. 32 - 37
• Main Authors: Hassin, Refael, Levin, Asaf
• Format: Journal Article
• Language: English
• Published: New York Wiley Subscription Services, Inc., A Wiley Company 01.08.2002; John Wiley & Sons
• Subjects: Applied sciences; Exact sciences and technology; network synthesis; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Teleprocessing networks. Isdn; Transmission and modulation (techniques and equipments); wavelength routing; WDM; NP hard problem; Connected graph; Wavelength division multiplexing; Routing; Approximation algorithm; Communication network; Wavelength
• ISSN: 0028-3045; 1097-0037
• DOI: 10.1002/net.10036

Consider a requirement graph whose vertices represent customers and an edge represents the need to route a unit of flow between its end vertices along a single path. All these flows are to be routed simultaneously. A solution network consists of a (multi)graph on the same set of vertices, such that it is possible to route simultaneously all of the required flows in such a way that no edge is used more than K times. The SYNTHESIS OF WAVELENGTH ROUTING NETWORK (SWRN) problem is to compute a solution network of a minimum number of edges. This problem has significant importance in the world of fiber‐optic networks where a link can carry a limited amount of different wavelengths and one is interested in finding a minimum‐cost network such that all the requirements can be carried in the network without changing the wavelength of a path at any of its internal vertices. In this paper, we prove that the SWRN problem is NP‐hard for any constant K (K ≥ 2). Then, we assume that GR is a clique with n vertices and we find an “almost” optimal solution network for all values of K (K = o(n)) and present a Min{(K + 1)/2, 2 + 2/(K − 1)}‐approximation algorithm for the general case and a 2‐approximation algorithm for d‐regular graphs. © 2002 Wiley Periodicals, Inc.