Efficient Schemes for Parallel Communication
Journal of the ACM (JACM)
Parallel hashing—an efficient implementation of shared memory
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Explicit expanders and the Ramanujan conjectures
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Constructing a perfect matching is in random NC
Combinatorica
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Randomized parallel communication (Preliminary Version)
PODC '82 Proceedings of the first ACM SIGACT-SIGOPS symposium on Principles of distributed computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
The electrical resistance of a graph captures its commute and cover times
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Network topology generators: degree-based vs. structural
Proceedings of the 2002 conference on Applications, technologies, architectures, and protocols for computer communications
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In a typical parallel or distributed computation model processors are connected by a sparse interconnection network. To establish open-line communication between pairs of processors that wish to communicate interactively, a set of disjoint paths has to be constructed on the network. Since communication needs vary in time, paths have to be dynamically constructed and destroyed.We study the complexity of constructing disjoint paths between given pairs of vertices on expander interconnection graphs. These graphs have been shown before to possess desirable properties for other communication tasks.We present a sufficient condition for the existence of &Kgr; ≤ np edge-disjoint paths connecting any set of &Kgr; pairs of vertices on an expander graph. We then show that the computational problem of constructing these paths lies in the classes Deterministic-P and Random-NC.Furthermore, we show that the set of paths can be constructed in probabilistic polylog time in the parallel-distributed model of computation, in which the n participating processors reside in the nodes of the communication graph and all communication is done through edges of the graph. Thus, the disjoint paths are constructed in the very computation model that uses them.Finally, we show how to apply variants of our parallel algorithms to find sets of vertex-disjoint paths when certain conditions are satisfied.