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On shortest paths and sorting

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Ellis L. JohnsonAuthors Info & Claims

ACM '72: Proceedings of the ACM annual conference - Volume 1

Pages 510 - 517

https://doi.org/10.1145/800193.569965

Published: 01 August 1972 Publication History

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Abstract

In finding shortest paths, the operation of finding, successively, a minimum from a list of numbers may require more work than the remainder of the algorithm. It is shown how algorithms from sorting literature can be used to accomplish this part of the shortest path algorithm. Bounds on the largest possible amount of work are established, and results of a computational study are reported.

References

[1]

Dantzig, G. B., "On the shortest route through a network", Management Science 6, 187 (1959).

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Google Scholar

[2]

Dijkstra, E. W., "A note on two problems in connection with graphs", Numerische Mathematik I, 269 (1959).

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Google Scholar

[3]

Floyd, R. W., "Algorithm 245, Treesort 3", CACM 7, 701 (1964).

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Google Scholar

[4]

Murchland, J. D., "The 'once-through' method of finding all shortest distances in a graph from a single origin", LBS-TNT-56. T, 1969, mimeographed technical report of London School of Economics, Transport Network Theory.

Google Scholar

[5]

Murchland, J. D., "An upper bound for the average candidate creation factor in arc lyne shortest distance calculations", 1971, Institut fur Angewandte Reaktorphysik, Karlsruhe, Germany.

Google Scholar

[6]

Williams, J. W. J., "Algorithm 232, heapsort", CACM 7, 347 (1964).

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Zhou XVenigalla MZhu S(2017)Bounding Box Approach to Network Pruning for Efficient Path Search through Large NetworksJournal of Computing in Civil Engineering10.1061/(ASCE)CP.1943-5487.000067531:5Online publication date: Sep-2017
https://doi.org/10.1061/(ASCE)CP.1943-5487.0000675
Picard JQueyranne M(2016)Selected Applications of Minimum Cuts in NetworksINFOR: Information Systems and Operational Research10.1080/03155986.1982.1173187620:4(394-422)Online publication date: 25-May-2016
https://doi.org/10.1080/03155986.1982.11731876
Minoux M(2009)On robust maximum flow with polyhedral uncertainty setsOptimization Letters10.1007/s11590-009-0116-y3:3(367-376)Online publication date: 14-Feb-2009
https://doi.org/10.1007/s11590-009-0116-y
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ACM '72: Proceedings of the ACM annual conference - Volume 1

August 1972

194 pages

ISBN:9781450374910

DOI:10.1145/800193

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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Association for Computing Machinery

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Published: 01 August 1972

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August 1, 1972

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Zhou XVenigalla MZhu S(2017)Bounding Box Approach to Network Pruning for Efficient Path Search through Large NetworksJournal of Computing in Civil Engineering10.1061/(ASCE)CP.1943-5487.000067531:5Online publication date: Sep-2017
https://doi.org/10.1061/(ASCE)CP.1943-5487.0000675
Picard JQueyranne M(2016)Selected Applications of Minimum Cuts in NetworksINFOR: Information Systems and Operational Research10.1080/03155986.1982.1173187620:4(394-422)Online publication date: 25-May-2016
https://doi.org/10.1080/03155986.1982.11731876
Minoux M(2009)On robust maximum flow with polyhedral uncertainty setsOptimization Letters10.1007/s11590-009-0116-y3:3(367-376)Online publication date: 14-Feb-2009
https://doi.org/10.1007/s11590-009-0116-y
Gallo GPallottino S(2009)Shortest path methods: A unifying approachNetflow at Pisa10.1007/BFb0121087(38-64)Online publication date: 26-Feb-2009
https://doi.org/10.1007/BFb0121087
Deo NPang C(2006)Shortest‐path algorithms: Taxonomy and annotationNetworks10.1002/net.323014020814:2(275-323)Online publication date: 11-Oct-2006
https://doi.org/10.1002/net.3230140208
Glover FGlover RKlingman D(2006)Computational study of an improved shortest path algorithmNetworks10.1002/net.323014010314:1(25-36)Online publication date: 11-Oct-2006
https://doi.org/10.1002/net.3230140103
Kershenbaum ABoorstyn R(2006)Centralized teleprocessing network designNetworks10.1002/net.323013021113:2(279-293)Online publication date: 11-Oct-2006
https://doi.org/10.1002/net.3230130211
Dial RGlover FKarney DKlingman D(2006)A computational analysis of alternative algorithms and labeling techniques for finding shortest path treesNetworks10.1002/net.32300903049:3(215-248)Online publication date: 11-Oct-2006
https://doi.org/10.1002/net.3230090304
Kershenbaum A(2006)Computing capacitated minimal spanning trees efficientlyNetworks10.1002/net.32300404034:4(299-310)Online publication date: 11-Oct-2006
https://doi.org/10.1002/net.3230040403
Klunder GPost H(2006)The shortest path problem on large‐scale real‐road networksNetworks10.1002/net.2013148:4(182-194)Online publication date: 30-Aug-2006
https://doi.org/10.1002/net.20131
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Improved algorithms for the k simple shortest paths and the replacement paths problems

Replacement paths and k simple shortest paths in unweighted directed graphs

Shortest Paths with Shortest Detours

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Improved algorithms for the k simple shortest paths and the replacement paths problems

Replacement paths and k simple shortest paths in unweighted directed graphs

Shortest Paths with Shortest Detours

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