The maximum k-colorable subgraph problem for chordal graphs
Information Processing Letters
Efficient routing in all-optical networks
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Improved access to optical bandwidth in trees
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
Constrained Bipartite Edge Coloring with Applications to Wavelength Routing
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
On-line Competive Algorithms for Call Admission in Optical Networks
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
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
Approximation Algorithms and Complexity Results for Path Problems in Trees of Rings
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Routing and Admission Control in Networks with Advance Reservations
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
WAE '00 Proceedings of the 4th International Workshop on Algorithm Engineering
Routing and wavelength assignment in generalized WDM tree networks of bounded degree
PCI'05 Proceedings of the 10th Panhellenic conference on Advances in Informatics
Wavelength assignment for satisfying maximal number of requests in all-optical networks
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
Maximizing the number of connections in multifiber WDM chain, ring and star networks
NETWORKING'05 Proceedings of the 4th IFIP-TC6 international conference on Networking Technologies, Services, and Protocols; Performance of Computer and Communication Networks; Mobile and Wireless Communication Systems
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Parameterized maximum path coloring
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Parameterized maximum path coloring
Theoretical Computer Science
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In optical networks with wavelength division multiplexing (WDM), multiple connections can share a link if they are transmitted on different wavelengths. We study the problem of satisfying a maximum number of connection requests in a directed tree network if only a limited number W of wavelengths are available. In optical networks without wavelength converters this is the maximum path coloring (MaxPC) problem, in networks with full wavelength conversion this is the maximum path packing (MaxPP) problem. MaxPC and MaxPP are shown to be polynomial-time solvable to optimality if the tree has height one or if both W and the degree of the tree are bounded by a constant. If either W or the degree of the tree is not bounded by a constant, MaxPC and MaxPP are proved NP-hard. Polynomial-time approximation algorithms with performance ratio 5/3 + Ɛ for arbitrarily small Ɛ are presented for the case W = 1, in which MaxPC and MaxPP are equivalent. For arbitrary W, a 2-approximation for MaxPP in arbitrary trees, a 1.58-approximation for MaxPC in trees of bounded degree, and a 2.22-approximation for MaxPC in arbitrary trees are obtained.