Data structures and network algorithms
Data structures and network algorithms
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Efficient routing in all-optical networks
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
On the k-coloring of intervals
Discrete Applied Mathematics
Efficient routing in optical networks
Journal of the ACM (JACM)
On-line call admission for high-speed networks
On-line call admission for high-speed networks
Online computation and competitive analysis
Online computation and competitive analysis
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Optimal wavelength routing on directed fiber trees
Theoretical Computer Science
Ring routing and wavelength translation
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
The complexity of path coloring and call scheduling
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Randomized path coloring on binary trees
Theoretical Computer Science
Colouring Paths in Directed Symmetric Trees with Applications to WDM 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
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
Methods and Problems of Wavelength-Routing in All-Optical Networks
Methods and Problems of Wavelength-Routing in All-Optical Networks
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
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Path problems such as the maximum edge-disjoint paths problem, the path coloring problem, and the maximum path coloring problem are relevant for resource allocation in communication networks, in particular all-optical networks. In this paper, it is shown that maximum path coloring can be solved optimally in polynomial time for bidirected generalized stars, even in the weighted case. Furthermore, the maximum edge-disjoint paths problem is proved NP-hard for complete graphs (undirected or bidirected), a constant-factor off-line approximation algorithm is presented for the weighted case, and an on-line algorithm with constant competitive ratio is given for the unweighted case. Finally, an open problem concerning the existence of routings that simultaneously minimize the maximum load and the number of colors is solved: an example for a graph and a set of requests is given such that any routing that minimizes the maximum load requires strictly more colors for path coloring than a routing that minimizes the number of colors.