Postman Problem Research Articles

Recent results on Arc Routing Problems: An annotated bibliography

AbstractArc 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. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010

On Chinese postman games where residents of each road pay the cost of their road

We study the extended Chinese postman (CP) cooperative game induced by a connected, weighted, undirected graph G, wherein a postman, starting from a post office location, needs to traverse all edges wherein players reside, before returning to the post-office. We characterize the graphs associated with all CP games in which the players on a road pay exactly the cost of the road at each core point, regardless of the number of players residing on the road, the location of the post-office and the edge-weight functions. Here, a road is a maximal path all of whose interior vertices have a degree equal to two in G. For this class of games, the core and nucleolus are Cartesian products of CP games induced by simple cyclic graphs, the core is determined by at most 2 n − 1 constraints and the nucleolus can be computed in O ( n 2 ) time.

Energy constrained multi-robot sensor-based coverage path planning using capacitated arc routing approach

Multi-robot sensor-based coverage path planning requires every point given in the workspace has to be covered at least by a sensor of a robot in the robot team. In this study, a novel algorithm was proposed for the sensor-based coverage of narrow environments by considering energy capacities of the robots. For this purpose, the environment was modeled by a Generalized Voronoi diagram-based graph to guarantee complete sensor-based coverage. Then, depending on the required arc set, a complete coverage route was created by using the Chinese Postman Problem or the Rural Postman Problem, and this route was partitioned among robots by considering energy capacities. Route partitioning was realized by modifying the Ulusoy partitioning algorithm which has polynomial complexity. This modification handles two different energy consumptions of mobile robots during sensor-based coverage, which was not considered before. The developed algorithm was coded in C++ and implemented on P3-DX mobile robots both in laboratory and in MobileSim simulation environments. It was shown that the convenient routes for energy constrained multi-robots could be generated by using the proposed algorithm in less than 1 s.

Chinese Postman Problem (CPP): solution methods and computational time

This paper proposes an algorithm to choose suitable methods to solve the Chinese Postman Problem (CPP). This study also concerns CPP computational time analysis, aiming to determine whether optimising methods can be used to solve real CPP instances with minimal computational time (polynomial time). The algorithm proposed is based on a literature review of the CPP. Regarding computational time analysis, two case studies were performed in a medium-sized city in Brazil. In addition, it was shown that for real problems (200 nodes) no significant differences exist between the computational time of the mathematical solutions for undirected, directed and mixed problems.

On the Use of Uniform Random Generation of Automata for Testing

Developing efficient and automatic testing techniques is one of the major challenges facing software validation community. In this paper, we show how a uniform random generation process of finite automata, developed in a recent work by Bassino and Nicaud, is relevant for many faces of automatic testing. The main contribution is to show how to combine two major testing approaches: model-based testing and random testing. This leads to a new testing technique successfully experimented on a realistic case study. We also illustrate how the power of random testing, applied on a Chinese Postman Problem implementation, points out an error in a well-known algorithm. Finally, we provide some statistics on model-based testing algorithms.

O problema do carteiro chinês, algoritmos exatos e um ambiente MVI para análise de suas instâncias: sistema XNÊS

Apresenta-se um estudo geral sobre o Problema do Carteiro Chinês (PCC), nas versões simétrica, orientada e mista, do ponto de vista dos algoritmos exatos até então publicados sobre o assunto. Para apresentar as soluções exatas das versões do problema, foram utilizadas as implementações exatas dos algoritmos de Sherafat (dos casos orientado e misto) com adaptações, e de Edmonds & Johnson (do simétrico) adaptada de Burkard & Derigs. O trabalho também apresenta as diferenças de comportamento dos métodos em situações bastante peculiares, através de um conjunto de instâncias testes com o objetivo de apurar mais detalhadamente o seu desempenho. Por fim, mostramos o software (Sistema XNÊS) idealizado para gerar grafos instâncias (simétricos, orientados e/ou mistos) e soluções exatas para estas versões do Problema do Carteiro Chinês (PCC). Implementa-se aqui uma versão de um modelo de geração de grafos no modo de Modelagem Visual Interativa (MVI), através de um editor específico de grafos com atributos e informações de efeitos visuais nos vértices e nas ligações. Este software pode ser usado como demonstração efetiva da importância do problema na academia, assim como um potencial analista de rotas de problemas semelhantes, ou até mesmo como verificador de instâncias das mais complicadas ou de razoável porte do PCC.

Maximum Likelihood Genome Assembly

Whole genome shotgun assembly is the process of taking many short sequenced segments (reads) and reconstructing the genome from which they originated. We demonstrate how the technique of bidirected network flow can be used to explicitly model the double-stranded nature of DNA for genome assembly. By combining an algorithm for the Chinese Postman Problem on bidirected graphs with the construction of a bidirected de Bruijn graph, we are able to find the shortest double-stranded DNA sequence that contains a given set of k-long DNA molecules. This is the first exact polynomial time algorithm for the assembly of a double-stranded genome. Furthermore, we propose a maximum likelihood framework for assembling the genome that is the most likely source of the reads, in lieu of the standard maximum parsimony approach (which finds the shortest genome subject to some constraints). In this setting, we give a bidirected network flow-based algorithm that, by taking advantage of high coverage, accurately estimates the copy counts of repeats in a genome. Our second algorithm combines these predicted copy counts with matepair data in order to assemble the reads into contigs. We run our algorithms on simulated read data from Escherichia coli and predict copy counts with extremely high accuracy, while assembling long contigs.

DNA computation for Chinese Postman Problem

Such new concepts as virtual weight and virtual node were proposed,and based on which,a novel algorithm based on DNA computation was designed to solve the Chinese Postman Problem(CPP).In the new proposed algorithm,all the feasible solutions of the CPP were obtained by utilizing the Polymerase Chain Reaction(PCR) techniques to eliminate false solutions from all the possible solutions,and then,the optimal solutions were extracted from those feasible solutions by utilizing surface-based techniques for DNA computation and fluorescence-labeling.The results indicate that the new algorithm has good characteristics such as simple encoding and readability.

Optimization of Municipal Solid Waste Collection System: Case Study

Curbside collection of municipal solid waste (MSW) constitutes a substantial portion of waste management cost. The utilization of operations research tools for the reduction of MSW collection costs in the Township of Millburn, N.J., was investigated. This research identified network models, specifically the Chinese postman problem algorithm as one of the approaches that could be used to evaluate the truck routes and the optimum sequence of each of these vehicles needed to collect the generated waste. The Township of Millburn has a population of 20,000 in approximately 7,000 households. The township divides the service area into three sections and collects waste twice a week from curbsides of single-family and two-2 family units using up to four trucks. Additional data, such as the number of houses per street and distances between intersections, were obtained from the Township and from Google Earth. Then with the aid of commercial software, the optimum routes for each of the trucks were obtained. Results from this optimization study were then compared with the current waste collection practice. Based on the case study results improvements to the current MSW collection procedure were proposed to the Township of Millburn, N.J.

Not being (super)thin or solid is hard: A study of grid Hamiltonicity

We give a systematic study of Hamiltonicity of grids — the graphs induced by finite subsets of vertices of the tilings of the plane with congruent regular convex polygons (triangles, squares, or hexagons). Summarizing and extending existing classification of the usual, “square”, grids, we give a comprehensive taxonomy of the grid graphs. For many classes of grid graphs we resolve the computational complexity of the Hamiltonian cycle problem. For graphs for which there exists a polynomial-time algorithm we give efficient algorithms to find a Hamiltonian cycle. We also establish, for any g ⩾ 6 , a one-to-one correspondence between Hamiltonian cycles in planar bipartite maximum-degree-3 graphs and Hamiltonian cycles in the class C g of girth-g planar maximum-degree-3 graphs. As applications of the correspondence, we show that for graphs in C g the Hamiltonian cycle problem is NP-complete and that for any N ⩾ 5 there exist graphs in C g that have exactly N Hamiltonian cycles. We also prove that for the graphs in C g , a Chinese Postman tour gives a ( 1 + 8 g ) -approximation to TSP, improving thereby the Christofides ratio when g > 16 . We show further that, in any graph, the tour obtained by Christofides' algorithm is not longer than a Chinese Postman tour.

Search for an immobile entity on a network

We consider the problem of searching for a single, uniformly distributed immobile entity on an undirected network. This problem differs from edge-covering problems, e.g., the Chinese Postman Problem (CPP), since the objective here is not to find the minimum length tour that covers all the edges at least once, but instead to minimize the expected time to find the entity. We introduce a heuristic algorithm to deal with the search process given that the entity is equally likely to be at any point on the network. Computational results are presented.

GENIIS, a New Hybrid Algorithm for Solving the Mixed Chinese Postman Problem

Mixed Chinese Postman Problem (MCPP) is a practical generalization of the classical Chinese Postman Problem (CPP) and it could be applied in many real world. Although MCPP is useful in terms of reality, MCPP has been proved to be a NP-complete problem. To find optimal solutions efficiently in MCPP, we can reduce searching space to be small effective searching space containing optimal solutions. We propose GENIIS methodology, which is a kind of hybrid algorithm combines the approximate algorithms and genetic algorithm. To get good solutions in the effective searching space, GENIIS uses approximate algorithm and genetic algorithm. This paper validates the usefulness of the proposed approach in a simulation. The results of our paper could be utilized to increase the efficiencies of network and transportation in business.

Hide‐and‐seek games on a tree to which Eulerian networks are attached

AbstractWe analyze the hide‐and‐seek game Γ(G) on certain networks G. The hider picks a hiding point yin Gand the searcher picks a unit speed path S(t) in G, starting at any point S(0). The payoff in this zero‐sum game is the capture time T = T(S,y) = min{t: S(t) = y}. Such games have been studied before, but mainly with the simplifying assumption that the searcher's starting point S(0) is specified and known to the hider. We call a network partly Eulerian if it consists of a tree (of length aand radius r) to which a finite number of disjoint Eulerian networks (of total length b) are attached, each at a single point. We show that for such networks, a strategy consisting equiprobably of a minimal (Chinese Postman) covering path and its reverse path is optimal for the searcher, while the optimal hider strategy is to assume that the searcher must start at the center of the tree, and to optimize in that (known) game. The value of the game Γ(G) is a+b/2 ‐r. This simplifies and extends a similar result of Dagan and Gal for search games on trees. © 2008 Wiley Periodicals, Inc. NETWORKS, 2008

Minimum cycle cover and Chinese postman problems on mixed graphs with bounded tree-width

Let M = ( V , E , A ) be a mixed graph with vertex set V , edge set E and arc set A . A cycle cover of M is a family C = { C 1 , … , C k } of cycles of M such that each edge/arc of M belongs to at least one cycle in C . The weight of C is ∑ i = 1 k | C i | . The minimum cycle cover problem is the following: given a strongly connected mixed graph M without bridges, find a cycle cover of M with weight as small as possible. The Chinese postman problem is: given a strongly connected mixed graph M , find a minimum length closed walk using all edges and arcs of M . These problems are NP-hard. We show that they can be solved in polynomial time if M has bounded tree-width.

Approximate Mechanisms for the Graphical TSP and Other Graph-Traversal Problems

Let G = (V,E) be a graph modeling a network in which each edge is owned by a selfish agent, which establishes the cost for traversing its edge (i.e., assigns a weight to its edge) by pursuing only its personal utility. In such a setting, we aim at designing approximate truthful mechanisms for several NP-hard traversal problems on G, such as the graphical traveling salesman problem, the rural postman problem, and the mixed Chinese postman problem, each of which in general requires an edge of G to be used several times. Thus, in game-theoretic terms, these are one-parameter problems, but with a peculiarity: the workload of each agent is a natural number. In this paper we refine the classical notion of monotonicity of an algorithm so as to capture exactly this property, and we then provide a general mechanism-design technique that guarantees this monotonicity and that allows one to compute efficiently the corresponding payments. In this way, we show that the former two problems and the latter one admit a 3/2...

Polarity and the complexity of the shooting experiment

We exhibit a polar relationship between two measures that have been proposed to evaluate the importance of TSP facets, the Kuhn–Gomory shooting experiment size and the probability of integrality in an augmented LP relaxation. The polarity establishes the complexity of performing the shooting experiment. We illustrate the resulting relationship on the Chinese postman and minimum spanning set problems.

Undirected postman problems with zigzagging option: A cutting-plane approach

The paper devises a new model and associated cutting-plane and branch-and-cut approaches for a variant of the undirected Chinese and rural postman problem where some of the edges offer the flexibility of either being serviced twice by two separate traversals or by a single zigzag traversal. The kernel of the proposed cutting-plane algorithm is a separation procedure for generalized blossom inequalities. We show that the currently best known separation procedure of Letchford, Reinelt and Theis [A faster exact separation algorithm for blossom inequalities. In: Nemhauser G, Bienstock D, editors, Integer programming and combinatorial optimization, vol. 3064. Berlin: Springer; 2004. (chapter 10)] is applicable and leads to a highly efficient solution approach which can handle large-scale problem instances.

DNA Computing Model Based on a New Scheme of Encoding Weight for Chinese Postman Problem

DNA Computing Model Based on a New Scheme of Encoding Weight for Chinese Postman Problem

Problema do carteiro chinês: escolha de métodos de solução e análise de tempos computacionais

O presente trabalho trata do problema do carteiro chinês (CPP). Primeiramente, por meio da estruturação e análise de uma revisão bibliográfica, propõe-se um algoritmo para auxiliar na escolha de métodos adequados a fim de se resolver o CPP. Em seguida, o algoritmo desenvolvido é utilizado na escolha de métodos para resolução do CPP em dois casos reais. O trabalho também verifica se, nos problemas práticos de logística urbana estudados, é válida uma premissa citada na literatura de que a complexidade do CPP com uma única entidade em problemas mistos é muito maior do que para problemas direcionados e não direcionados. Para isto, são selecionados casos reais de coleta de lixo e correios em uma cidade do interior paulista. Este trabalho conclui que, para problemas extraídos de situações logísticas reais, inexistem significativas diferenças entre o tempo computacional para a resolução dos modelos matemáticos com vistas à obtenção de grafos eulerianos não direcionados, direcionados e mistos.

A comprehensive problem for algorithm and paradigm visualization

The web site for algorithm visualization described in a previous article [4] has been extended to include the multi-stage Chinese Postman problem in the context of grid graphs. The various stages a...