### Abstract

Let N = (V, A, c, l) be an input network with node set V, arc set A, positive arc weight function c and nonnegative arc weight function l. Let σ be the amount of data to be transmitted. The quickest path problem is to find a routing path in N to transmit the given amount of data in minimum time. In a recent paper, Chen and Chin proposed this problem and developed algorithms for the single pair quickest path problem with time complexity O(re + rn log n), where n = |V|, e = |A|, and r is the number of distinct capacity values of N. In this paper, we first develop an alternative algorithm for the single pair quickest path problem with same time complexity and less space requirement. We then study the constrained quickest path problem and propose an O(re + rn log n) time algorithm. Finally, we develop an algorithm to enumerate the first m quickest paths to send a given amount of data from one node to another with time complexity O(rmne + rmn^{2} log n).

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

Pages (from-to) | 579-584 |

Number of pages | 6 |

Journal | Computers and Operations Research |

Volume | 18 |

Issue number | 6 |

DOIs | |

State | Published - 1991 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Information Systems and Management
- Management Science and Operations Research
- Applied Mathematics
- Modeling and Simulation
- Transportation

### Cite this

*Computers and Operations Research*,

*18*(6), 579-584. https://doi.org/10.1016/0305-0548(91)90063-W

**Algorithms for the quickest path problem and the enumeration of quickest paths.** / Rosen, J. B.; Sun, S. Z.; Xue, Guoliang.

Research output: Contribution to journal › Article

*Computers and Operations Research*, vol. 18, no. 6, pp. 579-584. https://doi.org/10.1016/0305-0548(91)90063-W

}

TY - JOUR

T1 - Algorithms for the quickest path problem and the enumeration of quickest paths

AU - Rosen, J. B.

AU - Sun, S. Z.

AU - Xue, Guoliang

PY - 1991

Y1 - 1991

N2 - Let N = (V, A, c, l) be an input network with node set V, arc set A, positive arc weight function c and nonnegative arc weight function l. Let σ be the amount of data to be transmitted. The quickest path problem is to find a routing path in N to transmit the given amount of data in minimum time. In a recent paper, Chen and Chin proposed this problem and developed algorithms for the single pair quickest path problem with time complexity O(re + rn log n), where n = |V|, e = |A|, and r is the number of distinct capacity values of N. In this paper, we first develop an alternative algorithm for the single pair quickest path problem with same time complexity and less space requirement. We then study the constrained quickest path problem and propose an O(re + rn log n) time algorithm. Finally, we develop an algorithm to enumerate the first m quickest paths to send a given amount of data from one node to another with time complexity O(rmne + rmn2 log n).

AB - Let N = (V, A, c, l) be an input network with node set V, arc set A, positive arc weight function c and nonnegative arc weight function l. Let σ be the amount of data to be transmitted. The quickest path problem is to find a routing path in N to transmit the given amount of data in minimum time. In a recent paper, Chen and Chin proposed this problem and developed algorithms for the single pair quickest path problem with time complexity O(re + rn log n), where n = |V|, e = |A|, and r is the number of distinct capacity values of N. In this paper, we first develop an alternative algorithm for the single pair quickest path problem with same time complexity and less space requirement. We then study the constrained quickest path problem and propose an O(re + rn log n) time algorithm. Finally, we develop an algorithm to enumerate the first m quickest paths to send a given amount of data from one node to another with time complexity O(rmne + rmn2 log n).

UR - http://www.scopus.com/inward/record.url?scp=0025862824&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025862824&partnerID=8YFLogxK

U2 - 10.1016/0305-0548(91)90063-W

DO - 10.1016/0305-0548(91)90063-W

M3 - Article

AN - SCOPUS:0025862824

VL - 18

SP - 579

EP - 584

JO - Surveys in Operations Research and Management Science

JF - Surveys in Operations Research and Management Science

SN - 0305-0548

IS - 6

ER -