Computing Shortest path and Minimum Spanning Tree under Uncertainty

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Tavassolian, Amir | 2019

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 51832 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Zarei, Alireza
Abstract:
Computing shortest paths and minimum spanning trees are basic and well-known problems in computer science and graph theory; also they have been considered as basic subroutines for many practical algorithms. There exists optimal algorithms for solving these problems when information about the basic graph is certain and specified. But, in real applications when the graph is obtained by using measurement tools which have limited computing precision, practically we are facing a graph in which locations of vertices or weights of edges are estimated.In such cases determining upper bounds or lower bounds for solutions of the shortest path and the minimum spanning tree are estimations of the deviation from the exact solutions of these two problems. In this type of modeling, each vertex of the graph is considered as a region indicating the region in which that vertex can be located, and our goal is to find the worst and the best solutions for the above mentioned problems in accordance with locations of placing each vertex in its allowable region. In this thesis, in addition to introducing and reviewing previous results in this domain, we will present new findings about some cases of these problems
Keywords:
Minimum Spanning Tree ; Shortest Path ; Uncertainty