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Constructing disjoint paths on expander graphs

Authors:

E. UpfalAuthors Info & Claims

STOC '87: Proceedings of the nineteenth annual ACM symposium on Theory of computing

Pages 264 - 273

https://doi.org/10.1145/28395.28424

Published: 01 January 1987 Publication History

Abstract

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 Κ ≤ n^p edge-disjoint paths connecting any set of Κ 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.

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Cited By

Haeupler BHershkowitz DTan Z(2024)New Structures and Algorithms for Length-Constrained Expander Decompositions2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00102(1634-1645)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00102
Nikoletseas SSpirakis P(2005)Expander properties in random regular graphs with edge faultsSTACS 9510.1007/3-540-59042-0_93(421-432)Online publication date: 1-Jun-2005
https://doi.org/10.1007/3-540-59042-0_93
Nikoletseas SPalem KSpirakis PYung M(2005)Short vertex disjoint paths and multiconnectivity in random graphs: Reliable network computingAutomata, Languages and Programming10.1007/3-540-58201-0_94(508-519)Online publication date: 29-May-2005
https://doi.org/10.1007/3-540-58201-0_94
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Constructing disjoint paths on expander graphs

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Published In

cover image ACM Conferences

STOC '87: Proceedings of the nineteenth annual ACM symposium on Theory of computing

January 1987

471 pages

ISBN:0897912217

DOI:10.1145/28395

Editor:
Alfred V. Aho

Copyright © 1987 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 January 1987

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STOC87: 19th Annual ACM Conference on Theory of Computing

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STOC '87 Paper Acceptance Rate 50 of 165 submissions, 30%;

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Cited By

Haeupler BHershkowitz DTan Z(2024)New Structures and Algorithms for Length-Constrained Expander Decompositions2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00102(1634-1645)Online publication date: 27-Oct-2024
https://doi.org/10.1109/FOCS61266.2024.00102
Nikoletseas SSpirakis P(2005)Expander properties in random regular graphs with edge faultsSTACS 9510.1007/3-540-59042-0_93(421-432)Online publication date: 1-Jun-2005
https://doi.org/10.1007/3-540-59042-0_93
Nikoletseas SPalem KSpirakis PYung M(2005)Short vertex disjoint paths and multiconnectivity in random graphs: Reliable network computingAutomata, Languages and Programming10.1007/3-540-58201-0_94(508-519)Online publication date: 29-May-2005
https://doi.org/10.1007/3-540-58201-0_94
Schwill A(2005)Nonblocking graphs: Greedy algorithms to compute disjoint pathsSTACS 9010.1007/3-540-52282-4_48(250-262)Online publication date: 6-Jun-2005
https://doi.org/10.1007/3-540-52282-4_48
Tangmunarunkit HGovindan RJamin SShenker SWillinger W(2002)Network topology generatorsACM SIGCOMM Computer Communication Review10.1145/964725.63304032:4(147-159)Online publication date: 19-Aug-2002
https://dl.acm.org/doi/10.1145/964725.633040
Tangmunarunkit HGovindan RJamin SShenker SWillinger WMathis MSteenkiste PBalakrishnan HPaxson V(2002)Network topology generatorsProceedings of the 2002 conference on Applications, technologies, architectures, and protocols for computer communications10.1145/633025.633040(147-159)Online publication date: 19-Aug-2002
https://dl.acm.org/doi/10.1145/633025.633040
Chandra ARaghavan PRuzzo WSmolensky R(1989)The electrical resistance of a graph captures its commute and cover timesProceedings of the twenty-first annual ACM symposium on Theory of computing10.1145/73007.73062(574-586)Online publication date: 1-Feb-1989
https://dl.acm.org/doi/10.1145/73007.73062
Schwill A(1989)Shortest edge-disjoint paths in graphsSTACS 8910.1007/BFb0029011(505-516)Online publication date: 1989
https://doi.org/10.1007/BFb0029011
Dahlhaus EHajnal PKarpinski M(1988)Optimal parallel algorithm for the Hamiltonian cycle problem on dense graphsProceedings of the 29th Annual Symposium on Foundations of Computer Science10.1109/SFCS.1988.21936(186-193)Online publication date: 24-Oct-1988
https://dl.acm.org/doi/10.1109/SFCS.1988.21936

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