A polyhedral approach to the rural postman problem

Corberán, Ángel; Sanchis, José M.

doi:10.1016/0377-2217(94)90398-0

Cited by 88 publications

(67 citation statements)

References 10 publications

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“…Both statements are with respect to the parameters "join set size" and "number of connected components in the input graph". 8 It is easy to see that the ≤ PPP m -equivalence of Eulerian Extension (EE) and Rural Postman given by Dorn et al [10] also holds for the parameters "number of components" and "number of components in the graph induced by the required arcs." Thus, a statement that is analogous to Theorem 4.3 holds for Rural Postman, when substituting Rural Postman for EE and substituting the parameter accordingly.…”

Section: Theorem 43 If the Problem Conjoining Bipartite Matching Ismentioning

confidence: 99%

“…Subsequent to RP's introduction [13,28] it has been shown NP-complete [23]. Heuristics and approximation algorithms have been presented [3,17,18,20,32] as well as exact exponential-time algorithms based on integer linear programs [7,8,19,25]. See also overview articles by Eiselt et al [14], by Assad and Golden [1] and the book edited by Dror [12].…”

Section: Introductionmentioning

confidence: 99%

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A New View on Rural Postman Based on Eulerian Extension and Matching

Sorge

Bevern

Niedermeier

et al. 2011

Lecture Notes in Computer Science

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We provide a new characterization of the NP-hard arc routing problem Rural Postman in terms of a constrained variant of minimum-weight perfect matching on bipartite graphs. To this end, we employ a parameterized equivalence between Rural Postman and Eulerian Extension, a natural arc addition problem in directed multigraphs. We indicate the NP-hardness of the introduced matching problem. In particular, we use the matching problem to make partial progress towards answering the open question about the parameterized complexity of Rural Postman with respect to the parameter "number of weakly connected components in the graph induced by the required arcs". This is a more than thirty years open and long-neglected question with significant practical relevance.

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Section: Theorem 43 If the Problem Conjoining Bipartite Matching Ismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New View on Rural Postman Based on Eulerian Extension and Matching

Sorge

Bevern

Niedermeier

et al. 2011

Lecture Notes in Computer Science

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“…K-C inequalities were introduced in Corberán & Sanchis (1994) for the undirected RPP and in Corberán, Romero & Sanchis (2003) they were generalized to the Mixed GRP in two families, the K-C and the K-C 02 inequalities. In this section we will study their generalization to the WGRP.…”

Section: K-c Inequalitiesmentioning

confidence: 99%

“…• R-odd cut inequalities (6) • K-C inequalities (7) • Honeycomb inequalities (11), if the subgraph of G C induced by the required links E ∪A R is balanced and the graph (Ā, TĀ) is 2-connected. Honeycomb 02 inequalities if, in addition, for each edge or arc (u, v), with node u of type O and node v of type I, the subgraph of G C induced by the required links plus two extra arcs from u to v is a balanced graph.…”

Section: E(s V \S)mentioning

confidence: 99%

The Windy General Routing Polyhedron: A Global View of Many Known Arc Routing Polyhedra

Corberán¹,

Plana²,

Sanchis³

2008

SIAM J. Discrete Math.

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The Windy Postman Problem consists of finding a minimum cost traversal of all the edges of an undirected graph with two costs associated with each edge, representing the costs of traversing it in each direction. In this paper we deal with the Windy General Routing Problem (WGRP), in which only a subset of edges must be traversed and a subset of vertices must be visited. This is also an NP-hard problem that generalizes many important Arc Routing Problems (ARP's) and has some interesting real-life applications. Here we study the description of the WGRP polyhedron, for which some general properties and some large families of facet-inducing inequalities are presented. Moreover, since the WGRP contains many well-known routing problems as special cases, this paper also provides a global view of their associated polyhedra. Finally, for the first time, some polyhedral results for several ARP's defined on mixed graphs formulated using two variables per edge are presented.

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“…Christofides et al [3] proposed a branchand-price method for the RPP. Branch-and-cut methods were also considered by Sanchis [16], Corberán and Sanchis [6], Letchford [13], and more recently by Ghiani and Laporte [8]. Benavent et al [2] were inspired by a property obtained by Win [17] for the windy version of the CPP to solve the WRPP.…”

Section: Introductionmentioning

confidence: 99%

A branch-and-price algorithm for the windy rural postman problem

2011

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Abstract. In this paper, we propose an exact solution method for the Windy Rural Postman Problem (WRPP). The motivation to study this problem comes from some real-life applications, such as garbage collecting in a predefined sector with hills, where the traversing or the servicing speed can change following the direction. We present a Dantzig-Wolfe decomposition and a branch-and-price algorithm to solve the WRPP. To the best of our knowledge, DantzigWolfe decomposition has never been used to solve that problem. The numerical results show that optimal solutions are found in a very reasonable amount of time on instances with up to 100 nodes and 180 edges.

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A polyhedral approach to the rural postman problem

Cited by 88 publications

References 10 publications

A New View on Rural Postman Based on Eulerian Extension and Matching

A New View on Rural Postman Based on Eulerian Extension and Matching

The Windy General Routing Polyhedron: A Global View of Many Known Arc Routing Polyhedra

A branch-and-price algorithm for the windy rural postman problem

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