TY - GEN

T1 - Tight bounds for wavelength assignment on trees of rings

AU - Bian, Zhengbing

AU - Gu, Qian Ping

AU - Zhou, Xiao

PY - 2005/12/1

Y1 - 2005/12/1

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 by at most 3L 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 3L upper bound is tight that there are instances of the WA problem that require at least 3L wavelengths even on a tree of rings with degree four. We also give a 3L and 2-approximation algorithm for the WA problem on a tree of rings with degree at most six. Previous results include: 4L (resp. 3L) 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 by at most 3L 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 3L upper bound is tight that there are instances of the WA problem that require at least 3L wavelengths even on a tree of rings with degree four. We also give a 3L and 2-approximation algorithm for the WA problem on a tree of rings with degree at most six. Previous results include: 4L (resp. 3L) 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

UR - http://www.scopus.com/inward/record.url?scp=33746316028&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746316028&partnerID=8YFLogxK

U2 - 10.1109/IPDPS.2005.433

DO - 10.1109/IPDPS.2005.433

M3 - Conference contribution

AN - SCOPUS:33746316028

SN - 0769523129

SN - 0769523129

SN - 9780769523125

T3 - Proceedings - 19th IEEE International Parallel and Distributed Processing Symposium, IPDPS 2005

BT - Proceedings - 19th IEEE International Parallel and Distributed Processing Symposium, IPDPS 2005

T2 - 19th IEEE International Parallel and Distributed Processing Symposium, IPDPS 2005

Y2 - 4 April 2005 through 8 April 2005

ER -