In this article we define inverse line graphs of directed graphs as a new framework for solving some classical network analysis problems. The extraction method and theories of inverse line graphs are explained in this article. It is shown that by changing the analysis space from the original directed graph to the inverse line graph, complex problems can be changed into simpler problems. We show the usefulness of the proposed framework in two particular applications: shortest path computations and the more general route planning. Considering the implementation result, we expect that this framework could be used in many more network analysis problems.
Abstract. The enormous increase in the number of vehicles in the cities makes plenty of problems including air pollution, noise pollution, and traffic jam. Overcoming these annoying issues needs a significant plan in urban management such as using modern techniques in public transportation systems. Sharing either cars or taxies is one of the most interesting ways that has been used in some countries recently. In this phenomenon, 2 or 3 people use other’s car or taxi. In this article, an innovative approach to share taxies is proposed, and it uses a Genetic Algorithm to determine the placement of travelers in taxies. Therefore, some taxis will be switched off, and this helps to decrease urban traffic jam in cities. The results present that the proposed model turns off 69.8 % of taxies, and also 27.8 % of them carry more than one passenger; hence, this confirms the performance of the proposed model.
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