Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Efficient routing in all-optical networks
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Optimal wavelength routing on directed fiber trees
Theoretical Computer Science
Improved access to optical bandwidth in trees
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Efficient routing and scheduling algorithms for optical networks
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Ring routing and wavelength translation
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Routing and path multicoloring
Information Processing Letters
Wavelength assignment and generalized interval graph coloring
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
On Shortest-Path All-Optical Networks without Wavelength Conversion Requirements
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Approximating Circular Arc Colouring and Bandwidth Allocation in All-Optical Ring Networks
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Efficient access to optical bandwidth
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Methods and Problems of Wavelength-Routing in All-Optical Networks
Methods and Problems of Wavelength-Routing in All-Optical Networks
Multicommodity demand flow in a tree
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
IEEE Journal on Selected Areas in Communications
Lighting fibers in a dark network
IEEE Journal on Selected Areas in Communications
On a noncooperative model for wavelength assignment in multifiber optical networks
IEEE/ACM Transactions on Networking (TON)
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We study wavelength assignment in an optical network where each fiber has a fixed capacity of @m wavelengths. Given demand routes, we aim to minimize the maximum ratio between the number of fibers deployed on a link e and the number of fibers required on the same link e when wavelength assignment is allowed to be fractional. Our main results are negative ones. We show that there is no constant-factor approximation unless NP@? ZPP. In addition, unless NP @? ZPTIME(n^p^o^l^y^l^o^g^n) we show that there is no log^@c@m approximation for any @c@?(0,1) and no log^@cm approximation for any @c@?(0,0.5) where m is the number of links in the network. Our analysis is based on the hardness of approximating the chromatic numbers. On the positive side, we present algorithms with approximation ratios O(logm+log@m), O(logD"m"a"x+log@m) and O(D"m"a"x) respectively, where D"m"a"x is the length of the longest path.