The generalized packet routing problem
Theoretical Computer Science
A faster strongly polynomial minimum cost flow algorithm
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
The token distribution problem
SIAM Journal on Computing
Load balancing, selection sorting on the hypercube
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
A note on the token distribution problem
Information Processing Letters
Handbook of theoretical computer science (vol. A)
Load balancing and routing on the hypercube and related networks
Journal of Parallel and Distributed Computing
Finding minimum-cost flows by double scaling
Mathematical Programming: Series A and B
Near-perfect Token Distribution
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
Strongly Adaptive Token Distribution
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
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There is given a graph, that models a communication network of a multiprocessor system, and there are tokens (jobs) allocated to nodes of the graph. The task is to distribute the tokens evenly, subject to the constraint that they may be moved only along the edges of the graph. The cost of a distribution strategy is measured as the total number of operations of moving a token along an edge. An algorithm for general graphs is developed, by reduction to a maximum-flow minimum-cost problem, that finds a cost-optimal distribution strategy, given a graph and an initial token allocation. The main result is an algorithm for graphs that are lines of nodes; it finds the distribution strategy in time O(n), for a line of n nodes.