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Titlebook: Hamiltonian Cycle Problem and Markov Chains; Vivek S. Borkar,Vladimir Ejov,Giang T. Nguyen Book 2012 Springer Science+Business Media, LLC

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发表于 2025-3-21 16:33:28 | 显示全部楼层 |阅读模式
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Titlebook: Hamiltonian Cycle Problem and Markov Chains;  Vivek S. Borkar,Vladimir Ejov,Giang T. Nguyen Book 2012 Springer Science+Business Media, LLC
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
doihttps://doi.org/10.1007/978-1-4614-3232-6
isbn_softcover978-1-4899-9227-7
isbn_ebook978-1-4614-3232-6Series ISSN 0884-8289 Series E-ISSN 2214-7934
issn_series 0884-8289
copyrightSpringer Science+Business Media, LLC 2012
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发表于 2025-3-22 00:15:37 | 显示全部楼层
Book 2012s, 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
发表于 2025-3-22 01:30:45 | 显示全部楼层
0884-8289 supplied in original studies.Includes supplementary materia.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 con
发表于 2025-3-22 04:47:18 | 显示全部楼层
发表于 2025-3-22 10:35:53 | 显示全部楼层
https://doi.org/10.1057/9780230376465particular, in the context of this book, we observe that in any given graph Hamiltonian cycles (if any) correspond to a family of spanning subgraphs inducing very special Markov chains whose probability transition matrices are a subset of permutation matrices possessing only a single ergodic class.
发表于 2025-3-22 13:21:19 | 显示全部楼层
https://doi.org/10.1007/978-3-031-59563-9ising the top-left element of the fundamental matrix . of an MDP associated with the given graph, over the space of feasible deterministic policies ... The conjecture that the same holds for the larger space .. remains open.
发表于 2025-3-22 19:28:47 | 显示全部楼层
https://doi.org/10.1007/978-3-030-55438-5ter 5, one can minimise the traces of the fundamental matrices to determine the Hamiltonicity of a given graph. While it is unclear whether the trace function offers an algorithmic advantage over the top-left element or the determinant functions, the trace operator is certainly well studied and frequently employed.
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发表于 2025-3-23 04:36:59 | 显示全部楼层
The Philosophy of Chinese Military Cultureexample, Meringer [77]). This offers an opportunity to study the whole populations of these graphs with the goal of understanding the special nature of those members of that population that correspond to non-Hamiltonian graphs.
发表于 2025-3-23 07:12:47 | 显示全部楼层
Book 2012the 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
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