Arc Routing Problems, Part II: The Rural Postman Problem

Eiselt, H. A.; Gendreau, Michel; Laporte, Gilbert

doi:10.1287/opre.43.3.399

Cited by 301 publications

(174 citation statements)

References 55 publications

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“…In contrast to Rural Postman, whose unweighted variant is NP-hard [12], we can show that EE and MEE are polynomial-time solvable. Altogether, our work complements and extends known results for WMEE with restricted weight function [11] and Rural Postman, for which mainly approximation, heuristic, and some polynomial-time algorithms for special cases are known [7,10].…”

Section: Introductionsupporting

confidence: 75%

“…This work focuses on the latter problem, which has applications in scheduling [11]. Furthermore, the various applications of Rural Postman [7] carry over to WMEE since both problems are equivalent.…”

Section: Introductionmentioning

confidence: 99%

“…EE is closely related to the well-known Chinese Postman problem [6] and the more general Rural Postman problem [7,12]. More specifically, Rural Postman and WMEE are "equivalent" (see Section 2 for details).…”

Section: Introductionmentioning

confidence: 99%

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Efficient Algorithms for Eulerian Extension

Dorn

Moser

Niedermeier

et al. 2010

Graph Theoretic Concepts in Computer Science

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Abstract. Eulerian extension problems aim at making a given (directed) (multi-)graph Eulerian by adding a minimum-cost set of edges (arcs). These problems have natural applications in scheduling and routing and are closely related to the Chinese Postman and Rural Postman problems. Our main result is to show that the NP-hard Weighted Multigraph Eulerian Extension is fixed-parameter tractable with respect to the number k of extension edges (arcs). For an n-vertex multigraph, the corresponding running time amounts to O(4 k · n 3 ). This implies a fixed-parameter tractability result for the "equivalent" Rural Postman problem. In addition, we present several polynomial-time algorithms for natural Eulerian extension problems.

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Section: Introductionsupporting

confidence: 75%

Section: Introductionmentioning

confidence: 99%

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Efficient Algorithms for Eulerian Extension

Dorn

Moser

Niedermeier

et al. 2010

Graph Theoretic Concepts in Computer Science

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“…This is not a restriction as there exists a simple way to transform an instance not satisfying this assumption into an equivalent one which does (see, e.g., Christofides et al [10] or Eiselt et al [13]). …”

Section: The Min-max K-vehicles Windy Rppmentioning

confidence: 99%

Min‐Max K‐vehicles windy rural postman problem

et al. 2009

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In this paper the Min-Max version of the Windy Rural Postman Problem with several vehicles is introduced. For this problem, in which the objective is to minimize the length of the longest tour in order to find a set of balanced tours for the vehicles, we present here an ILP formulation and study its associated polyhedron. Based on its partial description, a branch-and-cut algorithm has been implemented and computational results on a large set of instances are finally presented.

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“…Nessa fase, utilizam-se modelos baseados no problema do Carteiro Rural (PCR), onde se garante que o serviço será realizado com a passagem do "fumacê" por todos os quarteirões onde seu serviço foi requisitado, com o menor custo total no trajeto, [EGL95], [NEG 96], [EFC 2003]. …”

Section: Veículos "Fumacês"unclassified

Integração de sistemas computacionais e modelos logísticos de otimização para prevenção e combate à dengue

et al. 2008

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ResumoO uso do conhecimento da ciência moderna no sentido de aprimorar os esforços de combate a doenças transmitidas por animais, denominadas zoonoses, em regiões tropicais é uma preocupação considerada de grande relevância pelos gestores da OMS. Este trabalho apresenta o desenvolvimento de uma metodologia de planejamento logístico para prevenção e combate à dengue, baseada em sistemas Geográficos de Informação e sistemas de Apoio a Decisão com modelos incorporados de otimização. Apresentamos também, uma ferramenta computacional, baseada na Web, desktops e palms e poquets, capaz de aplicar tal metodologia. Estudos e testes piloto, nas cidades de Sobral e Fortaleza, Ceará foram realizados. Os resultados dessa aplicação computacional forneceram, após os testes, uma melhor visualização da dimensão do problema de coordenação do combate para os gestores da dengue, ou seja, foram plenamente exitosos nesses experimentos pioneiros.Palavras-chave: logística de combate a doenças tropicais; programação inteira; SADE; sistemas para Web. AbstractThe use of modern science knowledge towards improving the efforts to combat zoonoses -, diseases that are communicable by animals -, in tropical regions is a concern taken into account by the World Health Organization (WHO) officials. In this article we intend to present the development of a logistical planning methodology for the prevention and combat of dengue, based on Geographic Information Systems (GIS) and Decision Support Systems with optimization models incorporated. We also present a Web, desktop, palm and pocket-based computational framework tool for use as a support in the application of such methodology, which was tested in a pilot case in the city of Sobral and most recently in the city of Fortaleza, state of Ceará, Brazil, and that has been providing a better view of the dimension of the problems faced by the officials responsible for coordinating the combat of diseases caused by zoonoses, namely dengue.

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Arc Routing Problems, Part II: The Rural Postman Problem

Cited by 301 publications

References 55 publications

Efficient Algorithms for Eulerian Extension

Efficient Algorithms for Eulerian Extension

Min‐Max K‐vehicles windy rural postman problem

Integração de sistemas computacionais e modelos logísticos de otimização para prevenção e combate à dengue

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