The <i>mixed postman problem</i> consists of finding a minimum cost tour of a mixed graph <i>M</i> = (<i>V</i>,<i>E</i>,<i>A</i>) traversing all its edges and arcs at least once. We prove that two well-known linear programming relaxations of this problem are equivalent. The <i>extra cost</i> of a mixed postman tour <i>T</i> is the cost of <i>T</i> minus the cost of the edges and arcs of <i>M</i>. We prove that it is <i>NP</i>-hard to approximate the minimum extra cost of a mixed postman tour. A related problem, known as the <i>windy postman problem</i>, consists of finding a minimum cost tour of an undirected graph <i>G</i>=(<i>V</i>,<i>E</i>) traversing all its edges at least once, where the cost of an edge depends on the direction of traversal. We say that <i>G</i> is <i>windy postman perfect</i> if a certain <i>windy postman polyhedron O</i> (<i>G</i>) is integral. We prove that series-parallel undirected graphs are windy postman perfect, therefore solving a conjecture of Win. Given a mixed graph <i>M</i> = (<i>V</i>,<i>E</i>,<i>A</i>) and a subset <i>R</i> &#8838; <i>E</i> &#8746; <i>A</i>, we say that a mixed postman tour of <i>M</i> is <i>restricted</i> if it traverses the elements of <i>R</i> exactly once. The <i>restricted mixed postman problem</i> consists of finding a minimum cost restricted tour. We prove that this problem is <i>NP</i>-hard even if <i>R</i>=<i>A</i> and we restrict <i>M</i> to be planar, hence solving a conjecture of Veerasamy. We also prove that it is <i>NP</i>-complete to decide whether there exists a restricted tour even if <i>R</i>=<i>E</i> and we restrict <i>M</i> to be planar. The <i>edges postman problem</i> is the special case of the restricted mixed postman problem when <i>R</i>=<i>A</i>. We give a new class of valid inequalities for this problem. We introduce a relaxation of this problem, called the <i>b-join problem</i>, that can be solved in polynomial time. We give an algorithm which is simultaneously a 4/3-approximation algorithm for the edges postman problem, and a 2-approximation algorithm for the extra cost of a tour. The <i>arcs postman problem</i> is the special case of the restricted mixed postman problem when <i>R</i>=<i>E</i>. We introduce a class of necessary conditions for <i>M</i> to have an arcs postman tour, and we give a polynomial-time algorithm to decide whether one of these conditions holds. We give linear programming formulations of this problem for mixed graphs arising from windy postman perfect graphs, and mixed graphs whose arcs form a forest.

The <i>mixed postman problem</i> consists of finding a minimum cost tour of a mixed graph <i>M</i> = (<i>V</i>,<i>E</i>,<i>A</i>) traversing all its edges and arcs at least once. We prove that two well-known linear programming relaxations of this problem are equivalent. The <i>extra cost</i> of a mixed postman tour <i>T</i> is the cost of <i>T</i> minus the cost of the edges and arcs of <i>M</i>. We prove that it is <i>NP</i>-hard to approximate the minimum extra cost of a mixed postman tour. A related problem, known as the <i>windy postman problem</i>, consists of finding a minimum cost tour of an undirected graph <i>G</i>=(<i>V</i>,<i>E</i>) traversing all its edges at least once, where the cost of an edge depends on the direction of traversal. We say that <i>G</i> is <i>windy postman perfect</i> if a certain <i>windy postman polyhedron O</i> (<i>G</i>) is integral. We prove that series-parallel undirected graphs are windy postman perfect, therefore solving a conjecture of Win. Given a mixed graph <i>M</i> = (<i>V</i>,<i>E</i>,<i>A</i>) and a subset <i>R</i> &#8838; <i>E</i> &#8746; <i>A</i>, we say that a mixed postman tour of <i>M</i> is <i>restricted</i> if it traverses the elements of <i>R</i> exactly once. The <i>restricted mixed postman problem</i> consists of finding a minimum cost restricted tour. We prove that this problem is <i>NP</i>-hard even if <i>R</i>=<i>A</i> and we restrict <i>M</i> to be planar, hence solving a conjecture of Veerasamy. We also prove that it is <i>NP</i>-complete to decide whether there exists a restricted tour even if <i>R</i>=<i>E</i> and we restrict <i>M</i> to be planar. The <i>edges postman problem</i> is the special case of the restricted mixed postman problem when <i>R</i>=<i>A</i>. We give a new class of valid inequalities for this problem. We introduce a relaxation of this problem, called the <i>b-join problem</i>, that can be solved in polynomial time. We give an algorithm which is simultaneously a 4/3-approximation algorithm for the edges postman problem, and a 2-approximation algorithm for the extra cost of a tour. The <i>arcs postman problem</i> is the special case of the restricted mixed postman problem when <i>R</i>=<i>E</i>. We introduce a class of necessary conditions for <i>M</i> to have an arcs postman tour, and we give a polynomial-time algorithm to decide whether one of these conditions holds. We give linear programming formulations of this problem for mixed graphs arising from windy postman perfect graphs, and mixed graphs whose arcs form a forest.

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Paging starts with leaf 2. There is no leaf 1. Vita. Includes bibliographical references (leaves 165-185). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Paging starts with leaf 2. There is no leaf 1. Vita. Includes bibliographical references (leaves 165-185). Also available on the Internet.

Graph theory is a large mathematical discipline. Chinese postman problem falls under category of arc vehicle routing problems. Chinese postman problems are very extensive and difficult to calculate in practice. They belong to NP-hard problems. For this reason, heuristics are proposed to provide acceptably good solution in polynomial time. The focus of this thesis is to propose a randomized heuristic which does not follow deterministic rules but is ruled by random. Monte Carlo simulation is launched to find the best solution. Heuristic is formulated for undirected capacitated rural postman problem. It is programmed in VBA and validated on testing problems. At the end of the thesis is a case study about municipal garbage collection.

This study aims to answer whether a heuristic that trades cycles between the tours in a solution would show good results when trying to solve the Weighted k-Chinese Postman Problem for undirected graphs, of varying size, representing neighbourhoods in Sweden.A tabu search heuristic was implemented with each iteration consisting of giving a cycle from the most expensive tour to the cheapest. The heuristic performed increasingly well for graphs of increasing size, although the solution quality decreased when increasing the number of tours to be used in the solution. It is suspected that the cause for this behavior is due to the heuristic only giving cycles from the most expensive tour, not considering trading cycles from other tours in the solution. It is believed that a heuristic considering more than only the most expensive tour when trading cycles would produce even better solutions.

Increasing waste production is the reason why it is important to focus in more detail on profitable and cost side of waste economy. This diploma thesis deals with the area of garbage collection as a fundamental part during garbage their cumulation in a particular location and follow-up liquidation or preservation. At first the theoretical background of Chinese Postman Problem is described as a cornerstone for garbage collection models. Extensions of this problem have to be considered to be closer to reality. Then waste management in the city of Poděbrady is thoroughly described. In the final part of diploma thesis aforementioned theoretical models are applied on real data obtained from the city of Poděbrady waste department. Heuristic algorithms are an essential part of thesis as a replacement of optimizations models that cannot be used in some cases due to high requirements on computational time.

This master's thesis describes modified Chinese Postman Problems. These Problems are solved by (mixed) integer linear programming. The modified problems and also used approach (integer programming) belong at least to the NP complexity class. The thesis analyzes, compares and estimates computational complexity of each model. Based on this analysis, usability of described models for solving real-life problems is deduced. The models are focused on problems in urban environment. Therefore, it is possible to apply these models on problems like optimization of a waste collection or road maintenance. Graph and problem generator is programmed for purposes of this thesis.

Orientador: Paulo Morelato França / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-09T05:57:31Z (GMT). No. of bitstreams: 1 Usberti_FabioLuiz_M.pdf: 37565259 bytes, checksum: cddb8b852bd82318a8c784f1f223a076 (MD5) Previous issue date: 2007 / Resumo: Esse trabalho se dedicou ao estudo dos algoritmos para roteamento de leituristas, incluindo propostas de alteração que resultem na melhoria da qualidade dos resultados. A motivação é proveniente da alta demanda por soluções computacionais para esse problema, ainda pouco estudado devido às peculiaridades que lhe são inerentes. Encontram-se na literatura duas heurísticas, de estratégias distintas e antagônicas para esse problema. Uma das heurísticas procura construir a rota ignorando a restrição de capacidade, para posterior particionamento dessa rota em subrotas, cada qual destinada a um leiturista (¿route first, cluster second¿). A outra heurística, em uma abordagem inversa, primeiramente subdivide a região de trabalho dos leituristas, para posterior roteamento dessas partições (¿cluster first, route second¿). Essas duas heurísticas foram testadas exaustivamente, tornando possível localizar aspectos sujeitos à melhoria, dando origem a duas novas heurísticas. Foi gerada uma base de testes contendo 144 instâncias que simulam as condições reais de trabalho dos leituristas, classificadas de acordo com o tamanho e dificuldade. A partir das soluções provenientes dos quatro algoritmos foi possível analisá-los comparativamente, avaliando o melhor em um âmbito geral (envolvendo todos os algoritmos) e específico (algoritmos de mesmo tipo, ¿route first cluster second¿ ou ¿cluster first route second¿), segundo critérios de qualidade pré-definidos: número de rotas, tempo de percurso, violação da carga horária e tempo computacional. Os resultados revelam que os novos algoritmos foram melhores tanto na comparação específica quanto na comparação geral / Abstract: This work¿s main study object consists on algorithms for routing meter readers, from which proposals towards solution¿s improvement are made. The demand for computational results concerning this problem, added to literature little attention due to its inherited peculiarities, has been the outmost motivation. Two preexisting heuristics from literature, with distinct and antagonic strategies, are pointed out. One of these heuristics atempt to create a single route, dismissing the capacity restriction, and then partitionates this route into subroutes, each of them destinated to one meter reader (route first, cluster second). The other heuristic, in an inverse approach, first splits the meter reader¿s working area, and only then routes each of these partitions (cluster first, route second). The two heuristics were tested to exaustion, allowing enumeration of weak aspects subject to improvement. Therefore, two new heuristics were developed, based upon the originals, however adapted in order to outperform solution¿s quality. A testing base containing 144 instances was generated, simulating meter readers realistic labor¿s conditions, classified by size and difficulty. Through solutions provided by the four algorithms, comparison analyses have taken place, evaluating in a general (involving all algorithms) and specific manner (same kind algorithms, i.e., route first, cluster second or cluster first, route second), considering four predefined quality criteria: number of routes, deadheading time, violation of shiftwork time and computational time. Results revealed that the new algorithms achieved better solutions on specific and general comparisons / Mestrado / Automação / Mestre em Engenharia Elétrica

Economic retrenchment, social shifts, and technological changes endanger journalism's democratic role. Journalism education faces parallel threats. I review the state of journalism and education, linking the crisis to society's loss of story, framed philosophically by the Dewey-critical theory split over journalism and power. I explore the potential for renewing journalism and education with Carey's ritual model and Postman's restoration of storytelling. I then summarize existing major academic programs and suggest a new interdisciplinary curriculum for environmental journalism, a specialty well suited to experimental, democracy-centered education. The curriculum uses as pedagogy active and conversational learning and reflection. A graduate introductory course is detailed, followed by additional suggested classes that could form the basis of a graduate certificate program or, with further expansion, a graduate degree concentration.