Compact distributed data structures for adaptive routing
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Routing with polynomial communication-space trade-off
SIAM Journal on Discrete Mathematics
Gigabit networking
The virtual path layout problem in fast networks (extended abstract)
PODC '94 Proceedings of the thirteenth annual ACM symposium on Principles of distributed computing
The layout of virtual paths in ATM networks
IEEE/ACM Transactions on Networking (TON)
Optimal layouts on a chain ATM network
Discrete Applied Mathematics - Special issue: network communications broadcasting and gossiping
Integrated Broadband Networks; An Introduction to ATM-Based Networks
Integrated Broadband Networks; An Introduction to ATM-Based Networks
A Scalable Approach to Routing in ATM Networks
WDAG '94 Proceedings of the 8th International Workshop on Distributed Algorithms
Directed Virtual Path Layouts in ATM Networks
DISC '98 Proceedings of the 12th International Symposium on Distributed Computing
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
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This paper studies the average hop count measure for virtual path layouts of ATM and optical networks. Routing in the ATM and optical network models is based on covering the network with simple virtual paths, under some constraints on the allowed load (i.e., the number of paths that can share an edge). The hop count is the number of edges along the virtual path.Two basic results are established concerning the average hop count parameter. The first concerns comparing the maximum and average hop count measures assuming uniform all-to-all communication requirements. We develop a rather general connection between the two measures for virtual path layouts with bounded maximum load. This connection allows us to extend known lower bounds on the maximum hop count into ones on the average hop count for network families satisfying certain conditions, termed non-condensingly contractable (NCC) graph families. Using this characterization, we establish tight lower bounds on the average hop count of virtual path layouts with bounded maximum load for paths, cycles, and trees.Our second result is an algorithm for designing a virtual path layout of minimum average hop count for a given tree network with general (weighted) one-to-all requirements.