TY - JOUR

T1 - Efficient algorithms for wavelength assignment on trees of rings

AU - Bian, Zhengbing

AU - Gu, Qian Ping

AU - Zhou, Xiao

N1 - Funding Information:
The authors thank the anonymous referees for their constructive comments. This work was partially supported by the NSERC Research Grant of Canada and the Japan Society for the Promotion of Science (JSPS) Grant-In-Aid for Scientific Research.

PY - 2009/3/6

Y1 - 2009/3/6

N2 - A fundamental problem in communication networks is wavelength assignment (WA): given a set of routing paths on a network, assign a wavelength to each path such that the paths with the same wavelength are edge-disjoint, using the minimum number of wavelengths. The WA problem is NP-hard for a tree of rings network which is well used in practice. In this paper, we give an efficient algorithm which solves the WA problem on a tree of rings with an arbitrary (node) degree using at most 3 L wavelengths and achieves an approximation ratio of 2.75 asymptotically, where L is the maximum number of paths on any link in the network. The 3 L upper bound is tight since there are instances of the WA problem that require 3 L wavelengths even on a tree of rings with degree four. We also give a 3 L and 2-approximation (resp. 2.5-approximation) algorithm for the WA problem on a tree of rings with degree at most six (resp. eight). Previous results include: 4 L (resp. 3 L) wavelengths for trees of rings with arbitrary degrees (resp. degree at most eight), and 2-approximation (resp. 2.5-approximation) algorithm for trees of rings with degree four (resp. six).

AB - A fundamental problem in communication networks is wavelength assignment (WA): given a set of routing paths on a network, assign a wavelength to each path such that the paths with the same wavelength are edge-disjoint, using the minimum number of wavelengths. The WA problem is NP-hard for a tree of rings network which is well used in practice. In this paper, we give an efficient algorithm which solves the WA problem on a tree of rings with an arbitrary (node) degree using at most 3 L wavelengths and achieves an approximation ratio of 2.75 asymptotically, where L is the maximum number of paths on any link in the network. The 3 L upper bound is tight since there are instances of the WA problem that require 3 L wavelengths even on a tree of rings with degree four. We also give a 3 L and 2-approximation (resp. 2.5-approximation) algorithm for the WA problem on a tree of rings with degree at most six (resp. eight). Previous results include: 4 L (resp. 3 L) wavelengths for trees of rings with arbitrary degrees (resp. degree at most eight), and 2-approximation (resp. 2.5-approximation) algorithm for trees of rings with degree four (resp. six).

KW - Approximation algorithms

KW - Communication networks

KW - Path coloring

KW - Trees of rings

KW - Wavelength assignment

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U2 - 10.1016/j.dam.2008.04.021

DO - 10.1016/j.dam.2008.04.021

M3 - Article

AN - SCOPUS:60649087525

VL - 157

SP - 875

EP - 889

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 5

ER -