Markov Chain Based Algorithms For The Hamiltonian Cycle Problem

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Markov Chain Based Algorithms For The Hamiltonian Cycle Problem

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Author : Michael Haythorpe
language : en
Publisher:
Release Date : 2010

Markov Chain Based Algorithms For The Hamiltonian Cycle Problem written by Michael Haythorpe and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Hamiltonian systems categories.

Hamiltonian Cycle Problem And Markov Chains

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Author : Vivek S. Borkar
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-23

Hamiltonian Cycle Problem And Markov Chains written by Vivek S. Borkar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-23 with Business & Economics categories.

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 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 many research papers appearing in journals catering to disparate audiences. As a result, the published manuscripts are often written in a very terse manner and use disparate notation, thereby making it difficult for new researchers to make use of the many reported advances. Hence the main purpose of this book is to present a concise and yet easily accessible synthesis of the majority of the theoretical and algorithmic results obtained so far. In addition, the book discusses numerous open questions and problems that arise from this body of work and which are yet to be fully solved. The approach casts the Hamiltonian Cycle Problem in a mathematical framework that permits analytical concepts and techniques, not used hitherto in this context, to be brought to bear to further clarify both the underlying difficulty of NP-completeness of this problem 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 and are illustrated with numerous examples.

Operations Research Proceedings 2019

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Author : Janis S. Neufeld
language : en
Publisher: Springer Nature
Release Date : 2020-09-24

Operations Research Proceedings 2019 written by Janis S. Neufeld and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-24 with Business & Economics categories.

This book gathers a selection of peer-reviewed papers presented at the International Conference on Operations Research (OR 2019), which was held at Technische Universität Dresden, Germany, on September 4-6, 2019, and was jointly organized by the German Operations Research Society (GOR) the Austrian Operations Research Society (ÖGOR), and the Swiss Operational Research Society (SOR/ASRO). More than 600 scientists, practitioners and students from mathematics, computer science, business/economics and related fields attended the conference and presented more than 400 papers in plenary presentations, parallel topic streams, as well as special award sessions. The respective papers discuss classical mathematical optimization, statistics and simulation techniques. These are complemented by computer science methods, and by tools for processing data, designing and implementing information systems. The book also examines recent advances in information technology, which allow big data volumes to be processed and enable real-time predictive and prescriptive business analytics to drive decisions and actions. Lastly, it includes problems modeled and treated while taking into account uncertainty, risk management, behavioral issues, etc.

Controlled Markov Chains Graphs And Hamiltonicity

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Author : Jerzy A. Filar
language : en
Publisher: Now Publishers Inc
Release Date : 2007

Controlled Markov Chains Graphs And Hamiltonicity written by Jerzy A. Filar and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

"Controlled Markov Chains, Graphs & Hamiltonicity" summarizes a line of research that maps certain classical problems of discrete mathematics--such as the Hamiltonian cycle and the Traveling Salesman problems--into convex domains where continuum analysis can be carried out. (Mathematics)

Computational Complexity Of Counting And Sampling

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Author : Istvan Miklos
language : en
Publisher: CRC Press
Release Date : 2019-02-21

Computational Complexity Of Counting And Sampling written by Istvan Miklos and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-21 with Mathematics categories.

Computational Complexity of Counting and Sampling provides readers with comprehensive and detailed coverage of the subject of computational complexity. It is primarily geared toward researchers in enumerative combinatorics, discrete mathematics, and theoretical computer science. The book covers the following topics: Counting and sampling problems that are solvable in polynomial running time, including holographic algorithms; #P-complete counting problems; and approximation algorithms for counting and sampling. First, it opens with the basics, such as the theoretical computer science background and dynamic programming algorithms. Later, the book expands its scope to focus on advanced topics, like stochastic approximations of counting discrete mathematical objects and holographic algorithms. After finishing the book, readers will agree that the subject is well covered, as the book starts with the basics and gradually explores the more complex aspects of the topic. Features: Each chapter includes exercises and solutions Ideally written for researchers and scientists Covers all aspects of the topic, beginning with a solid introduction, before shifting to computational complexity’s more advanced features, with a focus on counting and sampling

Approximation And Complexity In Numerical Optimization

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Author : Panos M. Pardalos
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Approximation And Complexity In Numerical Optimization written by Panos M. Pardalos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Technology & Engineering categories.

There has been much recent progress in approximation algorithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. In discrete (or combinatorial) optimization many approaches have been developed recently that link the discrete universe to the continuous universe through geomet ric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. As a result new ap proximate algorithms have been discovered and many new computational approaches have been developed. Similarly, for many continuous nonconvex optimization prob lems, new approximate algorithms have been developed based on semidefinite pro gramming and new randomization techniques. On the other hand, computational complexity, originating from the interactions between computer science and numeri cal optimization, is one of the major theories that have revolutionized the approach to solving optimization problems and to analyzing their intrinsic difficulty. The main focus of complexity is the study of whether existing algorithms are efficient for the solution of problems, and which problems are likely to be tractable. The quest for developing efficient algorithms leads also to elegant general approaches for solving optimization problems, and reveals surprising connections among problems and their solutions. A conference on Approximation and Complexity in Numerical Optimization: Con tinuous and Discrete Problems was held during February 28 to March 2, 1999 at the Center for Applied Optimization of the University of Florida.

Proceedings Of The Fifth Annual Acm Siam Symposium On Discrete Algorithms

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Author :
language : en
Publisher: SIAM
Release Date : 1994-01-01

Proceedings Of The Fifth Annual Acm Siam Symposium On Discrete Algorithms written by and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Science categories.

The January 1994 Symposium was jointly sponsored by the ACM Special Interest Group for Automata and Computability Theory and the SIAM Activity Group on Discrete Mathematics. Among the topics in 79 (unrefereed) papers: comparing point sets under projection; on-line search in a simple polygon; low- degree tests; maximal empty ellipsoids; roots of a polynomial and its derivatives; dynamic algebraic algorithms; fast comparison of evolutionary trees; an efficient algorithm for dynamic text editing; and tight bounds for dynamic storage allocation. No index. Annotation copyright by Book News, Inc., Portland, OR

Survivability And Traffic Grooming In Wdm Optical Networks

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Author : Arun Somani
language : en
Publisher: Cambridge University Press
Release Date : 2006-01-19

Survivability And Traffic Grooming In Wdm Optical Networks written by Arun Somani and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-19 with Technology & Engineering categories.

The advent of fiber optic transmission systems and wavelength division multiplexing (WDM) have led to a dramatic increase in the usable bandwidth of single fiber systems. This book provides detailed coverage of survivability (dealing with the risk of losing large volumes of traffic data due to a failure of a node or a single fiber span) and traffic grooming (managing the increased complexity of smaller user requests over high capacity data pipes), both of which are key issues in modern optical networks. A framework is developed to deal with these problems in wide-area networks, where the topology used to service various high-bandwidth (but still small in relation to the capacity of the fiber) systems evolves toward making use of a general mesh. Effective solutions, exploiting complex optimization techniques, and heuristic methods are presented to keep network problems tractable. Newer networking technologies and efficient design methodologies are also described.

Network Science

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Author : Carlos Andre Reis Pinheiro
language : en
Publisher: John Wiley & Sons
Release Date : 2022-11-08

Network Science written by Carlos Andre Reis Pinheiro and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-08 with Computers categories.

Network Science Network Science offers comprehensive insight on network analysis and network optimization algorithms, with simple step-by-step guides and examples throughout, and a thorough introduction and history of network science, explaining the key concepts and the type of data needed for network analysis, ensuring a smooth learning experience for readers. It also includes a detailed introduction to multiple network optimization algorithms, including linear assignment, network flow and routing problems. The text is comprised of five chapters, focusing on subgraphs, network analysis, network optimization, and includes a list of case studies, those of which include influence factors in telecommunications, fraud detection in taxpayers, identifying the viral effect in purchasing, finding optimal routes considering public transportation systems, among many others. This insightful book shows how to apply algorithms to solve complex problems in real-life scenarios and shows the math behind these algorithms, enabling readers to learn how to develop them and scrutinize the results. Written by a highly qualified author with significant experience in the field, Network Science also includes information on: Sub-networks, covering connected components, bi-connected components, community detection, k-core decomposition, reach network, projection, nodes similarity and pattern matching Network centrality measures, covering degree, influence, clustering coefficient, closeness, betweenness, eigenvector, PageRank, hub and authority Network optimization, covering clique, cycle, linear assignment, minimum-cost network flow, maximum network flow problem, minimum cut, minimum spanning tree, path, shortest path, transitive closure, traveling salesman problem, vehicle routing problem and topological sort With in-depth and authoritative coverage of the subject and many case studies to convey concepts clearly, Network Science is a helpful training resource for professional and industry workers in, telecommunications, insurance, retail, banking, healthcare, public sector, among others, plus as a supplementary reading for an introductory Network Science course for undergraduate students.

High Performance Computing

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Author : Ana-Lucia Varbanescu
language : en
Publisher: Springer Nature
Release Date : 2022-05-29

High Performance Computing written by Ana-Lucia Varbanescu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-29 with Computers categories.

This book constitutes the refereed proceedings of the 37th International Conference on High Performance Computing, ISC High Performance 2022, held in Hamburg, Germany, during May 29 – June 2, 2022. The 18 full papers presented were carefully reviewed and selected from 53 submissions. The papers are categorized into the following topical sub-headings: Architecture, Networks, and Storage; Machine Learning, AI, Emerging Technologies; HPC Algorithms and Applications; Performance Modeling, Evaluation and Analysis; and Programming Environments and Systems Software.