### Abstract

Since the introduction of the Chinese Postman Problem (CPP), many variations on the same theme have been developed. In this paper we examine still another variation. The arcs of the graph are partitioned and a precedence relation defined, specifying the order in which the elements of the partition have to be traversed. We first examine the conditions for a feasible solution to the problem. Next, we specify the graph properties of the precedence partition that insure a polynomial complexity solution of O(N^{5}), where N is the number of nodes in the original graph. When the precedence relation on sets of arcs is general, we prove that the problem of finding the minimum length of feasible postman tour is NP‐complete.

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

Pages (from-to) | 283-294 |

Number of pages | 12 |

Journal | Networks |

Volume | 17 |

Issue number | 3 |

DOIs | |

State | Published - 1987 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Information Systems
- Computer Networks and Communications

### Cite this

*Networks*,

*17*(3), 283-294. https://doi.org/10.1002/net.3230170304

**Postman tour on a graph with precedence relation on arcs.** / Dror, Moshe; Stern, Helman; Trudeau, Pierre.

Research output: Contribution to journal › Article

*Networks*, vol. 17, no. 3, pp. 283-294. https://doi.org/10.1002/net.3230170304

}

TY - JOUR

T1 - Postman tour on a graph with precedence relation on arcs

AU - Dror, Moshe

AU - Stern, Helman

AU - Trudeau, Pierre

PY - 1987

Y1 - 1987

N2 - Since the introduction of the Chinese Postman Problem (CPP), many variations on the same theme have been developed. In this paper we examine still another variation. The arcs of the graph are partitioned and a precedence relation defined, specifying the order in which the elements of the partition have to be traversed. We first examine the conditions for a feasible solution to the problem. Next, we specify the graph properties of the precedence partition that insure a polynomial complexity solution of O(N5), where N is the number of nodes in the original graph. When the precedence relation on sets of arcs is general, we prove that the problem of finding the minimum length of feasible postman tour is NP‐complete.

AB - Since the introduction of the Chinese Postman Problem (CPP), many variations on the same theme have been developed. In this paper we examine still another variation. The arcs of the graph are partitioned and a precedence relation defined, specifying the order in which the elements of the partition have to be traversed. We first examine the conditions for a feasible solution to the problem. Next, we specify the graph properties of the precedence partition that insure a polynomial complexity solution of O(N5), where N is the number of nodes in the original graph. When the precedence relation on sets of arcs is general, we prove that the problem of finding the minimum length of feasible postman tour is NP‐complete.

UR - http://www.scopus.com/inward/record.url?scp=84987039902&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84987039902&partnerID=8YFLogxK

U2 - 10.1002/net.3230170304

DO - 10.1002/net.3230170304

M3 - Article

AN - SCOPUS:84987039902

VL - 17

SP - 283

EP - 294

JO - Networks

JF - Networks

SN - 0028-3045

IS - 3

ER -