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Polynomial-Time Highest-Gain Augmenting Path Algorithms for the Generalized Circulation Problem

This paper presents two new combinatorial algorithms for the generalized circulation problem. After an initial step in which all flow-generating cycles are canceled and excesses are created, both algorithms bring these excesses to the sink via highest-gain augmenting paths. Scaling is applied to the... Full description

Journal Title: Mathematics of operations research 1997-11-01, Vol.22 (4), p.793-802
Main Author: Goldfarb, Donald
Other Authors: Jin, Zhiying , Orlin, James B
Format: Electronic Article Electronic Article
Language: English
Subjects:
Publisher: Linthicum, MD: INFORMS
ID: ISSN: 0364-765X
Link: http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=2107561
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title: Polynomial-Time Highest-Gain Augmenting Path Algorithms for the Generalized Circulation Problem
format: Article
creator:
  • Goldfarb, Donald
  • Jin, Zhiying
  • Orlin, James B
subjects:
  • Algorithms
  • Analysis
  • Applied sciences
  • arc excess
  • Combinatorial analysis
  • Exact sciences and technology
  • excess scaling
  • Flows in networks. Combinatorial problems
  • generalized circulation
  • generalized maximum flow
  • Grants
  • highest-gain augmenting path
  • Integers
  • Linear programming
  • Mathematical procedures
  • Minimization of cost
  • Models
  • network flows
  • Operational research and scientific management
  • Operational research. Management science
  • Operations research
  • Optimal solutions
  • Polynomials
  • Research grants
  • Studies
  • Usage
ispartof: Mathematics of operations research, 1997-11-01, Vol.22 (4), p.793-802
description: This paper presents two new combinatorial algorithms for the generalized circulation problem. After an initial step in which all flow-generating cycles are canceled and excesses are created, both algorithms bring these excesses to the sink via highest-gain augmenting paths. Scaling is applied to the fixed amount of flow that the algorithms attempt to send to the sink, and both node and arc excesses are used. The algorithms have worst-case complexities of O ( m 2 ( m + n log n ) log B ), where n is the number of nodes, m is the number of arcs, and B is the largest integer used to represent the gain factors and capacities in the network. This bound is better than the previous best bound for a combinatorial algorithm for the generalized circulation problem, and if m = O ( n 4/3– ), it is better than the previous best bound for any algorithm for this problem.
language: eng
source:
identifier: ISSN: 0364-765X
fulltext: no_fulltext
issn:
  • 0364-765X
  • 1526-5471
url: Link


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descriptionThis paper presents two new combinatorial algorithms for the generalized circulation problem. After an initial step in which all flow-generating cycles are canceled and excesses are created, both algorithms bring these excesses to the sink via highest-gain augmenting paths. Scaling is applied to the fixed amount of flow that the algorithms attempt to send to the sink, and both node and arc excesses are used. The algorithms have worst-case complexities of O ( m 2 ( m + n log n ) log B ), where n is the number of nodes, m is the number of arcs, and B is the largest integer used to represent the gain factors and capacities in the network. This bound is better than the previous best bound for a combinatorial algorithm for the generalized circulation problem, and if m = O ( n 4/3– ), it is better than the previous best bound for any algorithm for this problem.
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subjectAlgorithms ; Analysis ; Applied sciences ; arc excess ; Combinatorial analysis ; Exact sciences and technology ; excess scaling ; Flows in networks. Combinatorial problems ; generalized circulation ; generalized maximum flow ; Grants ; highest-gain augmenting path ; Integers ; Linear programming ; Mathematical procedures ; Minimization of cost ; Models ; network flows ; Operational research and scientific management ; Operational research. Management science ; Operations research ; Optimal solutions ; Polynomials ; Research grants ; Studies ; Usage
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abstractThis paper presents two new combinatorial algorithms for the generalized circulation problem. After an initial step in which all flow-generating cycles are canceled and excesses are created, both algorithms bring these excesses to the sink via highest-gain augmenting paths. Scaling is applied to the fixed amount of flow that the algorithms attempt to send to the sink, and both node and arc excesses are used. The algorithms have worst-case complexities of O ( m 2 ( m + n log n ) log B ), where n is the number of nodes, m is the number of arcs, and B is the largest integer used to represent the gain factors and capacities in the network. This bound is better than the previous best bound for a combinatorial algorithm for the generalized circulation problem, and if m = O ( n 4/3– ), it is better than the previous best bound for any algorithm for this problem.
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