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An O(nm)-Time Network Simplex Algorithm for the Shortest Path Problem

We present an O ( nm )-time network simplex algorithm for finding a tree of shortest paths from a given node to all other nodes in a network of n nodes and m directed arcs or finding a directed cycle of negative length. The worst-case running time of this algorithm is as fast as that proved for any... Full description

Journal Title: Operations research 1999-05-01, Vol.47 (3), p.445-448
Main Author: Goldfarb, Donald
Other Authors: Jin, Zhiying
Format: Electronic Article Electronic Article
Language: English
Subjects:
Quelle: Alma/SFX Local Collection
Publisher: Linthicum, MD: INFORMS
ID: ISSN: 0030-364X
Link: http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=1952094
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title: An O(nm)-Time Network Simplex Algorithm for the Shortest Path Problem
format: Article
creator:
  • Goldfarb, Donald
  • Jin, Zhiying
subjects:
  • Algorithms
  • analysis of algorithms
  • Applied sciences
  • computational complexity
  • distance algorithms
  • Exact sciences and technology
  • Flows in networks. Combinatorial problems
  • general shortest paths
  • linear algorithms
  • Mathematical programming
  • Mathematics
  • Minimization of cost
  • network simplex
  • networks/graphs
  • Operational research and scientific management
  • Operational research. Management science
  • Overestimates
  • Path analysis
  • Polynomials
  • programming
  • Simplex method
  • strongly polynomial
ispartof: Operations research, 1999-05-01, Vol.47 (3), p.445-448
description: We present an O ( nm )-time network simplex algorithm for finding a tree of shortest paths from a given node to all other nodes in a network of n nodes and m directed arcs or finding a directed cycle of negative length. The worst-case running time of this algorithm is as fast as that proved for any strongly polynomial algorithm and faster than that proved for any previously proposed simplex algorithm for this problem. We also show that this algorithm can be implemented in O ( nlogn ) time using O (( m / logn ) + n ) exclusive read–exclusive write processors of a parallel random access machine.
language: eng
source: Alma/SFX Local Collection
identifier: ISSN: 0030-364X
fulltext: fulltext
issn:
  • 0030-364X
  • 1526-5463
url: Link


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titleAn O(nm)-Time Network Simplex Algorithm for the Shortest Path Problem
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descriptionWe present an O ( nm )-time network simplex algorithm for finding a tree of shortest paths from a given node to all other nodes in a network of n nodes and m directed arcs or finding a directed cycle of negative length. The worst-case running time of this algorithm is as fast as that proved for any strongly polynomial algorithm and faster than that proved for any previously proposed simplex algorithm for this problem. We also show that this algorithm can be implemented in O ( nlogn ) time using O (( m / logn ) + n ) exclusive read–exclusive write processors of a parallel random access machine.
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subjectAlgorithms ; analysis of algorithms ; Applied sciences ; computational complexity ; distance algorithms ; Exact sciences and technology ; Flows in networks. Combinatorial problems ; general shortest paths ; linear algorithms ; Mathematical programming ; Mathematics ; Minimization of cost ; network simplex ; networks/graphs ; Operational research and scientific management ; Operational research. Management science ; Overestimates ; Path analysis ; Polynomials ; programming ; Simplex method ; strongly polynomial
ispartofOperations research, 1999-05-01, Vol.47 (3), p.445-448
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abstractWe present an O ( nm )-time network simplex algorithm for finding a tree of shortest paths from a given node to all other nodes in a network of n nodes and m directed arcs or finding a directed cycle of negative length. The worst-case running time of this algorithm is as fast as that proved for any strongly polynomial algorithm and faster than that proved for any previously proposed simplex algorithm for this problem. We also show that this algorithm can be implemented in O ( nlogn ) time using O (( m / logn ) + n ) exclusive read–exclusive write processors of a parallel random access machine.
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