Improved access to optical bandwidth in trees
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Scheduling multicasts on unit-capacity trees and meshes
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Wavelength conversion in optical networks
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Randomized path coloring on binary trees
Theoretical Computer Science
Bandwidth allocation in WDM tree networks
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
On Shortest-Path All-Optical Networks without Wavelength Conversion Requirements
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Randomized path coloring on binary trees
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
WAE '99 Proceedings of the 3rd International Workshop on Algorithm Engineering
Approximating Call-Scheduling Makespan in All-Optical Networks
WG '00 Proceedings of the 26th International Workshop on Graph-Theoretic Concepts in Computer Science
Recent Advances in Wavelength Routing
SOFSEM '01 Proceedings of the 28th Conference on Current Trends in Theory and Practice of Informatics Piestany: Theory and Practice of Informatics
Short length menger's theorem and reliable optical routing
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Scheduling multicasts on unit-capacity trees and meshes
Journal of Computer and System Sciences
A 2-approximation algorithm for path coloring on a restricted class of trees of rings
Journal of Algorithms
Tight Bounds for Wavelength Assignment on Trees of Rings
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Papers - Volume 01
Path problems in generalized stars, complete graphs, and brick wall graphs
Discrete Applied Mathematics - Special issue: Efficient algorithms
Short length Menger's theorem and reliable optical routing
Theoretical Computer Science
Inapproximability and approximability of minimal tree routing and coloring
Journal of Discrete Algorithms
Efficient algorithms for wavelength assignment on trees of rings
Discrete Applied Mathematics
Path problems in generalized stars, complete graphs, and brick wall graphs
Discrete Applied Mathematics - Special issue: Efficient algorithms
Paths coloring algorithms in mesh networks
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
Complexity of minimal tree routing and coloring
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
Approximation algorithms for path coloring in trees
Efficient Approximation and Online Algorithms
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In the minimum path coloring problem, we are given a list of pairs of vertices of a graph. We are asked to connect each pair by a colored path. Paths of the same color must be edge disjoint. Our objective is to minimize the number of colors used. This problem was raised by A. Aggarwal et al. (1994) and P. Raghavan and E. Upfal (1994) as a model for routing in all-optical networks. It is also related to questions in circuit routing. In this paper, we improve the O(ln N) approximation result of J. Kleinberg and E. Tardos (1995) for path coloring on the N/spl times/N mesh. We give an O(1) approximation algorithm to the number of colors needed, and a poly(ln ln N) approximation algorithm to the choice of paths and colors. To the best of our knowledge, these are the first sub-logarithmic bounds for any network other than trees, rings, or trees of rings. Our results are based on developing new techniques for randomized rounding. These techniques iteratively improve a fractional solution until it approaches integrality. They are motivated by the method used by F.T. Leighton, B.M. Maggs, and S.B. Rao (1994) for packet routing.