On the capacity of disjointly shared networks
Computer Networks and ISDN Systems
Random walks, Gaussian processes and list structures
Theoretical Computer Science
European Journal of Combinatorics
Efficient routing in all-optical networks
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Dynamic analysis of some relational databases parameters
Theoretical Computer Science - Special volume on mathematical analysis of algorithms (dedicated to D. E. Knuth)
A note on optical routing on trees
Information Processing Letters
Routing a permutation in the hypercube by two sets of edge disjoint paths
Journal of Parallel and Distributed Computing
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
Ring routing and wavelength translation
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Colouring Paths in Directed Symmetric Trees with Applications to WDM Routing
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
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
Journal of Discrete Algorithms
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In this paper we first show that the permutation-path coloring problem is NP-hard even for very restrictive instances like involutions, which are permutations that contain only cycles of length at most two, on both binary trees and on trees having only two vertices with degree greater than two, and for circular permutations, which are permutations that contain exactly one cycle, on trees with maximum degree greater than or equal to 4. We calculate a lower bound on the average complexity of the permutation-path coloring problem on arbitrary networks. Then we give combinatorial and asymptotic results for the permutation-path coloring problem on linear networks in order to show that the average number of colors needed to color any permutation on a linear network on n vertices is n/4 + o(n). We extend these results and obtain an upper bound on the average complexity of the permutation-path coloring problem on arbitrary trees, obtaining exact results in the case of generalized star trees. Finally we explain how to extend these results for the involutions-path coloring problem on arbitrary trees.