Finding Longest Paths on Special Classes of Graphs

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Afreshteh, Vahid Reza | 2017

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 51166 (19)
University: Sharif University of Technology
Department: Computer Engineering
Advisor(s): Zarrabi-Zadeh, Hamid
Abstract:
In this research, we consider the problem of finding longest paths in some special classes of graphs. This problem is NP-hard in general case. It has been proven that there is no constant factor polynomial time approximation algorithm for this problem, unless P = NP. Therefore, the problem is usually solved for special classes of graphs.In this research, we focus on finding longest paths in solid grids, and propose a factor 3/4 approximation algorithm. Our algorithm improves the best current result which has an approximation factor of 2/ 3 . As a side result, we also propose a linear time algorithm for finding Hamiltonian cycle in a subset of Hamiltonian solid grids which improves the current best O(n4)-time algorithm
Keywords:
Approximate Algorithm ; Hamiltonian Cycle Problem ; Longest Path ; Longest Cycle ; Hamiltonian Path ; Grid Graphs ; Solid Grid Graphs