书目名称 | Hamiltonian Cycle Problem and Markov Chains | 编辑 | Vivek S. Borkar,Vladimir Ejov,Giang T. Nguyen | 视频video | | 概述 | Concise, readable synthesis of important yet scattered research to date.Discusses problems yet to be fully solved.Provides many examples not supplied in original studies.Includes supplementary materia | 丛书名称 | International Series in Operations Research & Management Science | 图书封面 |  | 描述 | .This research monograph summarizes a line of research that maps certain classical problems of discrete mathematics and operations research - such as the Hamiltonian Cycle and the Travelling Salesman Problems - into convex domains where continuum analysis can be carried out. Arguably, the inherent difficulty of these, now classical, problems stems precisely from the discrete nature of domains in which these problems are posed. The convexification of domains underpinning these results is achieved by assigning probabilistic interpretation to key elements of the original deterministic problems. In particular, the approaches summarized here build on a technique that embeds Hamiltonian Cycle and Travelling Salesman Problems in a structured singularly perturbed Markov decision process. The unifying idea is to interpret subgraphs traced out by deterministic policies (including Hamiltonian cycles, if any) as extreme points of a convex polyhedron in a space filled with randomized policies..The above innovative approach has now evolved to the point where there are many, both theoretical and algorithmic, results that exploit the nexus between graph theoretic structures and both probabilistic | 出版日期 | Book 2012 | 关键词 | Combinatorial Optimization; Graphing; Hamiltonian Cycle Problem; Markov Chains; Mathematical Programming | 版次 | 1 | doi | https://doi.org/10.1007/978-1-4614-3232-6 | isbn_softcover | 978-1-4899-9227-7 | isbn_ebook | 978-1-4614-3232-6Series ISSN 0884-8289 Series E-ISSN 2214-7934 | issn_series | 0884-8289 | copyright | Springer Science+Business Media, LLC 2012 |
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