Efficient communication strategies for ad-hoc wireless networks (extended abstract)
Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures
Optimal bounds for matching routing on trees
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Delayed path coupling and generating random permutations via distributed stochastic processes
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Parametric permutation routing via matchings
Nordic Journal of Computing
End-to-end packet-scheduling in wireless ad-hoc networks
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Efficient bufferless packet switching on trees and leveled networks
Journal of Parallel and Distributed Computing
Routing Numbers of Cycles, Complete Bipartite Graphs, and Hypercubes
SIAM Journal on Discrete Mathematics
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
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A class of routing problems on connected graphs $G$ is considered. Initially, each vertex $v$ of $G$ is occupied by a ``pebble'' that has a unique destination $\pi (v)$ in $G$ (so that $\pi$ is a permutation of the vertices of $G$). It is required that all the pebbles be routed to their respective destinations by performing a sequence of moves of the following type: A disjoint set of edges is selected, and the pebbles at each edge's endpoints are interchanged. The problem of interest is to minimize the number of steps required for any possible permutation $\pi$. This paper investigates this routing problem for a variety of graphs $G$, including trees, complete graphs, hypercubes, Cartesian products of graphs, expander graphs, and Cayley graphs. In addition, this routing problem is related to certain network flow problems, and to several graph invariants including diameter, eigenvalues, and expansion coefficients.