Efficient routing in all-optical networks
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Randomized algorithms
Optical networks: a practical perspective
Optical networks: a practical perspective
Chernoff-Hoeffding bounds for applications with limited independence
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Improved access to optical bandwidth in trees
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Constrained Bipartite Edge Coloring with Applications to Wavelength Routing
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
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 Wavelength Routing on Directed Fiber Trees
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Efficient access to optical bandwidth
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Call Scheduling in Trees, Rings and Meshes
HICSS '97 Proceedings of the 30th Hawaii International Conference on System Sciences: Software Technology and Architecture - Volume 1
Path problems in generalized stars, complete graphs, and brick wall graphs
Discrete Applied Mathematics - Special issue: Efficient algorithms
Path problems in generalized stars, complete graphs, and brick wall graphs
Discrete Applied Mathematics - Special issue: Efficient algorithms
Approximation algorithms for path coloring in trees
Efficient Approximation and Online Algorithms
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Motivated by the problem of WDM routing in all-optical networks, we study the following NP-hard problem. We are given a directed binary tree T and a set R of directed paths on T. We wish to assign colors to paths of R, in such way that no two paths that share a directed arc of T are assigned the same color, and the total number of colors used is minimized. Our results are expressed in terms of the depth of the tree and of the maximum load l of R, i.e. the maximum number of paths that go through a directed arc of T. So far, only deterministic greedy algorithms have been presented for the problem. The best known algorithm colors any set R of maximum load l using at most 5l/3 colors. Alternatively, we say that this algorithm has performance ratio 5/3. It is also known that no deterministic greedy algorithm can achieve a performance ratio better than 5/3. In this paper we define the class of greedy algorithms that use randomization. We study their limitations and prove that, with high probability, randomized greedy algorithms cannot achieve a performance ratio better than 3/2 when applied for binary trees of depth Ω(l), and 1.293-o(1) when applied for binary trees of constant depth. Exploiting inherent properties of randomized greedy algorithms, we obtain the first randomized algorithm for the problem that uses at most 7l/5 + o(l) colors for coloring any set of paths of maximum load l on binary trees of depth O(l1/3-ε), with high probability. We also present an existential upper bound of 7l/5 + o(l) that holds on any binary tree. For the analysis of our bounds we develop tail inequalities for random variables following hypergeometrical probability distributions that might be of their own interest.