The forwarding index of communication networks
IEEE Transactions on Information Theory
On forwarding indices of networks
Discrete Applied Mathematics
Complexity of the forwarding index problem
SIAM Journal on Discrete Mathematics
Efficient routing in all-optical networks
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Discrete Applied Mathematics
Optimal wavelength-routed multicasting
Discrete Applied Mathematics
All-to-all routing and coloring in weighted trees of rings
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Efficient Collective Communication in Optical Networks
ICALP '96 Proceedings of the 23rd 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
Optical All-to-All Communication in Inflated Networks
WG '98 Proceedings of the 24th International Workshop on Graph-Theoretic Concepts in Computer Science
The maximum edge-disjoint paths problem in complete graphs
Theoretical Computer Science
On bounded load routings for modeling k-regular connection topologies
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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Motivated by wavelength-assignment problems for all-to-all traffic in optical networks, we study graph parameters related to sets of paths connecting all pairs of vertices. We consider sets of both undirected and directed paths, under minimisation criteria known as edge congestion and wavelength count; this gives rise to four parameters of a graph G: its edge forwarding index @p(G), arc forwarding index @p-(G), undirected optical index w(G), and directed optical index w-(G). In the paper we address two long-standing open problems: whether the equality @p-(G)=w-(G) holds for all graphs, and whether indices @p(G) and w(G) are hard to compute. For the first problem, we give an example of a family of planar graphs {G"k} such that @p-(G"k)w-(G"k). For the second problem, we show that determining either @p(G) or w(G) is NP-hard.