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The Resource Hamiltonian cycle problem and markov chains, Vivek S. Borkar...[et al.], (electronic resource)
Hamiltonian cycle problem and markov chains, Vivek S. Borkar...[et al.], (electronic resource)
Resource Information
The item Hamiltonian cycle problem and markov chains, Vivek S. Borkar...[et al.], (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Hamiltonian cycle problem and markov chains, Vivek S. Borkar...[et al.], (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 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 the reported results is achieved by assigning probabilistic interpretation to key elements of the original deterministic problems. In particular, approaches summarized here build on a technique that embeds Hamiltonian Cycle and Traveling 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 and algebraic entities of related Markov chains. The latter include moments of first return times, limiting frequencies of visits to nodes, or the spectra of certain matrices traditionally associated with the analysis of Markov chains. However, these results and algorithms are dispersed over more than fifteen research papers appearing in journals catering to disparate audiences such as: MOR, Random Structures and Algorithms, SIAM J. on Discrete Mathematics, Optimization, J. of Mathematical Analysis and Applications and some others. Furthermore, because of the evolution of this topic and specific orientation of these journals, the published manuscripts are often written in a very terse manner and use disparate notation. As such it is difficult for new researchers to make use of the many advances reported in these papers. Hence the main purpose of this book is to present a concise and yet, well written, synthesis of the majority of the theoretical and algorithmic results obtained so far. In addition the book will discuss numerous open questions and problems that arise from this body of work and which are yet to be fully solved. The authors believe that their approach casts the Hamiltonian Cycle and Traveling Salesman problems in a mathematical framework that permits analytical concepts and techniques, not used hitherto in their context, to be brought to bear to further clarify both the underlying difficulty of NPcompleteness of these problems and the relative exceptionality of truly difficult instances. Finally, the material is arranged in such a manner that the introductory chapters require very little mathematical background and discuss instances of graphs with interesting structures that motivated a lot of the research in this topic. More difficult results are introduced later but, unlike the research manuscripts where they were originally proved, are illustrated with numerous examples
 Language
 eng
 Extent
 1 online resource (xiv, 201 p.)
 Contents

 Illustrative Graphs
 Intriguing Properties
 Markov Chains
 Markov Decision Processes
 Determinants
 Traces
 Linear Programming Based Algorithms
 Interior Point and CrossEntropy Algorithms
 Selfsimilar Structure and Hamiltonicity
 Graph Enumeration
 Isbn
 9781461432326
 Label
 Hamiltonian cycle problem and markov chains
 Title
 Hamiltonian cycle problem and markov chains
 Statement of responsibility
 Vivek S. Borkar...[et al.]
 Subject

 Hamiltonian systems
 Distribution (Probability theory).
 Markov processes
 Economics/Management Science
 Probability Theory and Stochastic Processes
 Hamiltonian systems
 Affaires
 Electronic books
 Markov processes
 Economics/Management Science.
 Markov processes
 Operations Research, Management Science
 Hamiltonian systems
 Mathematical optimization.
 Hamiltonian systems
 Markov processes
 Operations Research, Management Science.
 Operations Research/Decision Theory.
 Economics.
 Hamiltonian systems
 Electronic resources
 MATHEMATICS / Differential Equations / General
 Science économique
 Markov processes
 Operations Research/Decision Theory
 Markov processes
 Optimization
 Probability Theory and Stochastic Processes.
 Optimization.
 Hamiltonian systems
 Language
 eng
 Summary
 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 the reported results is achieved by assigning probabilistic interpretation to key elements of the original deterministic problems. In particular, approaches summarized here build on a technique that embeds Hamiltonian Cycle and Traveling 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 and algebraic entities of related Markov chains. The latter include moments of first return times, limiting frequencies of visits to nodes, or the spectra of certain matrices traditionally associated with the analysis of Markov chains. However, these results and algorithms are dispersed over more than fifteen research papers appearing in journals catering to disparate audiences such as: MOR, Random Structures and Algorithms, SIAM J. on Discrete Mathematics, Optimization, J. of Mathematical Analysis and Applications and some others. Furthermore, because of the evolution of this topic and specific orientation of these journals, the published manuscripts are often written in a very terse manner and use disparate notation. As such it is difficult for new researchers to make use of the many advances reported in these papers. Hence the main purpose of this book is to present a concise and yet, well written, synthesis of the majority of the theoretical and algorithmic results obtained so far. In addition the book will discuss numerous open questions and problems that arise from this body of work and which are yet to be fully solved. The authors believe that their approach casts the Hamiltonian Cycle and Traveling Salesman problems in a mathematical framework that permits analytical concepts and techniques, not used hitherto in their context, to be brought to bear to further clarify both the underlying difficulty of NPcompleteness of these problems and the relative exceptionality of truly difficult instances. Finally, the material is arranged in such a manner that the introductory chapters require very little mathematical background and discuss instances of graphs with interesting structures that motivated a lot of the research in this topic. More difficult results are introduced later but, unlike the research manuscripts where they were originally proved, are illustrated with numerous examples
 Cataloging source
 GW5XE
 Image bit depth
 0
 LC call number
 QA614.83
 LC item number
 .H36 2012
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName

 SpringerLink
 Borkar, Vivek S
 Series statement
 International Series in Operations Research & Management Science,
 Series volume
 171
 http://library.link/vocab/subjectName

 Hamiltonian systems
 Markov processes
 MATHEMATICS / Differential Equations / General
 Economics/Management Science
 Operations Research/Decision Theory
 Operations Research, Management Science
 Optimization
 Probability Theory and Stochastic Processes
 Hamiltonian systems
 Markov processes
 Science économique
 Affaires
 Label
 Hamiltonian cycle problem and markov chains, Vivek S. Borkar...[et al.], (electronic resource)
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Illustrative Graphs  Intriguing Properties  Markov Chains  Markov Decision Processes  Determinants  Traces  Linear Programming Based Algorithms  Interior Point and CrossEntropy Algorithms  Selfsimilar Structure and Hamiltonicity  Graph Enumeration
 Dimensions
 unknown
 Extent
 1 online resource (xiv, 201 p.)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Isbn
 9781461432326
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number

 9786613698056
 10.1007/9781461432326
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 Stock number
 369805
 System control number

 (OCoLC)792942621
 (OCoLC)ocn792942621
 Label
 Hamiltonian cycle problem and markov chains, Vivek S. Borkar...[et al.], (electronic resource)
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Illustrative Graphs  Intriguing Properties  Markov Chains  Markov Decision Processes  Determinants  Traces  Linear Programming Based Algorithms  Interior Point and CrossEntropy Algorithms  Selfsimilar Structure and Hamiltonicity  Graph Enumeration
 Dimensions
 unknown
 Extent
 1 online resource (xiv, 201 p.)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Isbn
 9781461432326
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number

 9786613698056
 10.1007/9781461432326
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 Stock number
 369805
 System control number

 (OCoLC)792942621
 (OCoLC)ocn792942621
Subject
 Affaires
 Distribution (Probability theory).
 Economics.
 Economics/Management Science
 Economics/Management Science.
 Electronic books
 Electronic resources
 Hamiltonian systems
 Hamiltonian systems
 Hamiltonian systems
 Hamiltonian systems
 Hamiltonian systems
 Hamiltonian systems
 MATHEMATICS / Differential Equations / General
 Markov processes
 Markov processes
 Markov processes
 Markov processes
 Markov processes
 Markov processes
 Mathematical optimization.
 Operations Research, Management Science
 Operations Research, Management Science.
 Operations Research/Decision Theory
 Operations Research/Decision Theory.
 Optimization
 Optimization.
 Probability Theory and Stochastic Processes
 Probability Theory and Stochastic Processes.
 Science économique
Genre
Member of
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.bu.edu/portal/Hamiltoniancycleproblemandmarkovchains/RKljGP7Zmk4/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.bu.edu/portal/Hamiltoniancycleproblemandmarkovchains/RKljGP7Zmk4/">Hamiltonian cycle problem and markov chains, Vivek S. Borkar...[et al.], (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.bu.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.bu.edu/">Boston University Libraries</a></span></span></span></span></div>