Solving the hierarchical Chinese postman problem as a rural postman problem

Cabral, Edgar Alberto; Gendreau, Michel; Ghiani, Gianpaolo; Laporte, Gilbert

doi:10.1016/s0377-2217(02)00813-5

Cited by 32 publications

(24 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…See also overview articles by Eiselt et al [14], by Assad and Golden [1] and the book edited by Dror [12]. There is also a number of papers that evaluate algorithms for RP in practical settings [5,31]. However, we are not aware of studies in the realm of parameterized complexity except in the context of Eulerian extensions.…”

Section: Related Workmentioning

confidence: 99%

A new view on Rural Postman based on Eulerian Extension and Matching

Sorge

Bevern

Niedermeier

et al. 2012

Journal of Discrete Algorithms

View full text Add to dashboard Cite

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 NPhardness 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.

show abstract

Section: Related Workmentioning

confidence: 99%

A new view on Rural Postman based on Eulerian Extension and Matching

Sorge

Bevern

Niedermeier

et al. 2012

Journal of Discrete Algorithms

View full text Add to dashboard Cite

show abstract

“…5 Also observe that if E is an Eulerian extension for G, then E \ A(t) is an Eulerian extension for G + A(t) and, thus, it suffices to show the properties in Theorem 2.1 for maximal trails in Eulerian extensions. These properties will mainly be proven by taking such a trail in an Eulerian extension and "shortcutting" it such that the Eulerian extension still connects all components and retains the balance of every vertex.…”

Section: The Structure Of Minimum-weight Eulerian Extensionsmentioning

confidence: 99%

“…Consider a solution E to I EEA that also contains the arcs (1, 3), (3,5) to E, and add arcs from all remaining sources to their corresponding targets that reside in the same component to obtain a solution to I EE . Also, every solution to I EE has to connect the connected component W 1 1 to the rest of the graph.…”

Section: Removing Advicementioning

confidence: 99%

“…Given a directed, arc-weighted graph G and a subset R of its arcs (called "required arcs"), the task is to find a minimum-cost closed walk in G that visits all arcs of R. The practical applications of RP include snow plowing, garbage collection, and mail delivery [1,3,5,12,14,30]. Recently, it has been observed that RP is closely related (more precisely, "parameterized equivalent") to the arc addition problem Eulerian Extension (EE) [10].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Sorge

Bevern

Niedermeier

et al. 2011

Lecture Notes in Computer Science

View full text Add to dashboard Cite

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.

show abstract

“…In the latter article, other variants of the HCPP are also discussed. Finally, in Cabral et al [34] a transformation of the HCPP into the RPP is proposed. Computational results assessing the computational value of the transformation are also included.…”

Section: Other Cpp Variants the Generalized Chinesementioning

confidence: 99%

Recent results on Arc Routing Problems: An annotated bibliography

Corberán

Prins

2010

Networks

View full text Add to dashboard Cite

Arc routing problems are vehicle routing problems in which the tasks to be performed are located on some arcs or edges of a network, e.g., spreading salt on a road or collecting municipal refuse in a street. They have been much less studied than node routing problems but impressive developments have been achieved in the last decade. The objective of this article is to survey these recent results and to provide an annotated bibliography. Except for a few references, the period surveyed starts from the publication of the book "Arc routing: theory, solutions and applications", edited by Dror in 2000. The article is made up of two main parts: one on uncapacitated (single vehicle) problems derived from the Chinese Postman Problem, the Rural Postman Problem, and the General Routing Problem; and one on multivehicle or capacitated problems such as the Capacitated Arc Routing Problem.

show abstract

Solving the hierarchical Chinese postman problem as a rural postman problem

Cited by 32 publications

References 12 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

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

Recent results on Arc Routing Problems: An annotated bibliography

Contact Info

Product

Resources

About