### Abstract

A new shortest chain algorithm is developed for finding shortest or longest chains from one node to all other nodes in a connected network. The network is first transformed into a directed network. The algorithm constructs an acyclic auxiliary shortest (longest) chain network from the directed network, using the concepts of minimum cost and remaining degree of nodes in an attempt to make several "parallel" decisions at each step. The twofold decision process causes faster convergence to the optimum solution than with a version of the algorithm using only the minimum cumulative cost criteria, or with node labeling techniques. The algorithm works on networks with all cost coefficients either nonnegative or nonpositive, i.e., mixed costs are not allowed.

Original language | English (US) |
---|---|

Pages (from-to) | 111-120 |

Number of pages | 10 |

Journal | Applied Mathematics and Computation |

Volume | 37 |

Issue number | 2 |

DOIs | |

State | Published - 1990 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Numerical Analysis

### Cite this

**A new O(n ^{2}) shortest chain algorithm.** / Waissi, Gary.

Research output: Contribution to journal › Article

^{2}) shortest chain algorithm',

*Applied Mathematics and Computation*, vol. 37, no. 2, pp. 111-120. https://doi.org/10.1016/0096-3003(90)90039-6

}

TY - JOUR

T1 - A new O(n2) shortest chain algorithm

AU - Waissi, Gary

PY - 1990

Y1 - 1990

N2 - A new shortest chain algorithm is developed for finding shortest or longest chains from one node to all other nodes in a connected network. The network is first transformed into a directed network. The algorithm constructs an acyclic auxiliary shortest (longest) chain network from the directed network, using the concepts of minimum cost and remaining degree of nodes in an attempt to make several "parallel" decisions at each step. The twofold decision process causes faster convergence to the optimum solution than with a version of the algorithm using only the minimum cumulative cost criteria, or with node labeling techniques. The algorithm works on networks with all cost coefficients either nonnegative or nonpositive, i.e., mixed costs are not allowed.

AB - A new shortest chain algorithm is developed for finding shortest or longest chains from one node to all other nodes in a connected network. The network is first transformed into a directed network. The algorithm constructs an acyclic auxiliary shortest (longest) chain network from the directed network, using the concepts of minimum cost and remaining degree of nodes in an attempt to make several "parallel" decisions at each step. The twofold decision process causes faster convergence to the optimum solution than with a version of the algorithm using only the minimum cumulative cost criteria, or with node labeling techniques. The algorithm works on networks with all cost coefficients either nonnegative or nonpositive, i.e., mixed costs are not allowed.

UR - http://www.scopus.com/inward/record.url?scp=45149135699&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=45149135699&partnerID=8YFLogxK

U2 - 10.1016/0096-3003(90)90039-6

DO - 10.1016/0096-3003(90)90039-6

M3 - Article

VL - 37

SP - 111

EP - 120

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 2

ER -