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A Review of Solid Waste Management Modelling
Published in Hans-Werner Gottinger, Economic Models and Applications of Solid Waste Management, 1991
The single-route continuous problem is called the “Chinese-postman” problem. It is defined as finding the minimum distance continuous tour through a network which travels all arcs at least once. Thus the Chinese-postman problem is an arc-covering problem while the travelling salesman problem is a node-covering problem. Recent developments in the Chinesepostman problem using graph theory point to quick and efficient methods of solution.
Collection and Transportation of Solid Waste
Published in Charles R. Rhyner, Leander J. Schwartz, Robert B. Wenger, Mary G. Kohrell, Waste Management and Resource Recovery, 2017
Charles R. Rhyner, Leander J. Schwartz, Robert B. Wenger, Mary G. Kohrell
Similarly, a classical mathematical problem underlies the arc routing and scheduling problem. Called the Chinese postman problem, its objective is to find a minimum distance tour a postman would traverse through a street network in order to deliver the mail to the residents living on those streets.
Optimal Graph Traversals
Published in Jonathan L. Gross, Jay Yellen, Mark Anderson, Graph Theory and Its Applications, 2018
Jonathan L. Gross, Jay Yellen, Mark Anderson
Variations of the Chinese Postman Problem arise in numerous applications. These include garbage collection and street sweeping; snow-plowing; line-painting down the center of each street; police-car patrolling; census taking; and computer-driven plotting of a network.
Finite-time consensus for multi-agent systems with nonlinear dynamics under Euler digraph via pinning control
Published in International Journal of Systems Science, 2021
Xiangdong Liu, Shengchao He, Pingli Lu, Haikuo Liu, Changkun Du
From the perspective of topological structure, the undirected connected graph is the simplest and commonest case. The asymptotic consensus issue with some special diagraph which is strongly connected and containing directed spanning tree have been studied in Olfati-Saber and Murray (2004) and Ren and Beard (2005). In this paper, we introduce the Euler diagraph. As we know, an Euler graph has an even number of edges connected to each of its vertices. This type of graph was introduced in 1736 to solve the Konigsberger bridge problem (Bondy & Murty, 2010). From then on, many scholars focus on studying the property of Euler graph, and apply it to many practical problems such as Chinese postman problem, Euler travel problem, and Eulerian graph in the application of the distribution line. Later, researchers construct Eulerian network model, which is widely used in the National Airspace System to solve the air traffic flow in congested areas.