On the 1.1 edge-coloring of multigraphs
SIAM Journal on Discrete Mathematics
Architectures for linear lightwave networks
Architectures for linear lightwave networks
Efficient routing in all-optical networks
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Efficient routing in optical networks
Journal of the ACM (JACM)
A note on optical routing on trees
Information Processing Letters
Optical networks: a practical perspective
Optical networks: a practical perspective
On-line routing in all-optical networks
Theoretical Computer Science
Optimal wavelength routing on directed fiber trees
Theoretical Computer Science
Improved bounds for all optical routing
Proceedings of the sixth 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
Efficient collective communication in optical networks
Theoretical Computer Science
The complexity of path coloring and call scheduling
Theoretical Computer Science
Edge coloring of bipartite graphs with constraints
Theoretical Computer Science
Randomized path coloring on binary trees
Theoretical Computer Science
Fractional Path Coloring with Applications to WDM Networks
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Colouring Paths in Directed Symmetric Trees with Applications to WDM Routing
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Randomized Lower Bounds for Online Path Coloring
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
Disjoint paths in densely embedded graphs
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
Graphs and Hypergraphs
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The study of the path coloring problem is motivated by the allocation of optical bandwidth to communication requests in all-optical networks that utilize Wavelength Division Multiplexing (WDM). WDM technology establishes communication between pairs of network nodes by establishing transmitter-receiver paths and assigning wavelengths to each path so that no two paths going through the same fiber link use the same wavelength. Optical bandwidth is the number of distinct wavelengths. Since state-of-the-art technology allows for a limited number of wavelengths, the engineering problem to be solved is to establish communication minimizing the total number of wavelengths used. This is known as the wavelength routing problem. In the case where the underlying network is a tree, it is equivalent to the path coloring problem. We survey recent advances on the path coloring problem in both undirected and bidirected trees. We present hardness results and lower bounds for the general problem covering also the special case of sets of symmetric paths (corresponding to the important case of symmetric communication). We give an overview of the main ideas of deterministic greedy algorithms and point out their limitations. For bidirected trees, we present recent results about the use of randomization for path coloring and outline approximation algorithms that find path colorings by exploiting fractional path colorings. Also, we discuss upper and lower bounds on the performance of on-line algorithms.