Hamiltonian Cycle Problem and Markov Chains

Online-Ressource (XIV, 201p. 82 illus., 31 illus. in color, digital)

International Series in Operations Research & Management Science ; 171

Description based upon print version of record

Preface; Acknowledgements; Contents; Part I Motivating Phenomena; Chapter 1 Illustrative Graphs; 1.1 The Graph That Started It All; 1.2 A Sample of Distinctive Graphs; 1.3 Co-spectral Graphs; Chapter 2 Intriguing Properties; 2.1 Preliminaries and Notation; 2.2 Fractal-like Structure of Graphs; 2.3 Invariants of Graphs; Part II Probabilistic Approaches; Chapter 3 Markov Chains; 3.1 Introduction; 3.2 Markov Chains and Perturbations; 3.3 Hitting Times and the Fundamental Matrix; 3.4 Hamiltonian Cycles as Hitting Time Variance Minimisers; Chapter 4 Markov Decision Processes; 4.1 Introduction

4.2 Markov Decision Processes4.3 Occupational Measures; 4.4 Extreme Points and 1-randomised Policies; 4.5 A Parameter-Free Model; Part III Optimisation; Chapter 5 Determinants; 5.1 Introduction; 5.2 Optimality at Hamiltonian Cycles; 5.2.1 Unperturbed Case; 5.2.2 Perturbed Case; Chapter 6 Traces; 6.1 Introduction; 6.2 Optimality at Hamiltonian Cycles; 6.2.1 Unperturbed Case; 6.2.2 Perturbed Case; Part IV Algorithms; Chapter 7 Linear Programming Based Algorithms; 7.1 Introduction; 7.2 Branch and Fix Method; 7.3 An Algorithm that Implements the Branch and FixMethod; 7.4 Wedge Constraints

7.5 The Wedged-MIP heuristicChapter 8 Interior Point and Cross-Entropy Algorithms; 8.1 Introduction; 8.2 Interior Point Method Algorithm; 8.3 Cross-Entropy Algorithm; 8.4 Open Algorithmic Problems; Part V Geometric Approaches; Chapter 9 Self-similar Structure and Hamiltonicity; 9.1 Introduction; 9.2 Preliminaries; 9.3 Self-similar Multifilar Structure; 9.4 Self-similarity and Hamiltonicity; Chapter 10 Graph Enumeration; 10.1 Introduction; 10.2 Subdivision-equivalent Edges; 10.3 Enumerating Cubic Bridge Graphs; References; Index;

10.1007/978-1-4614-3232-6 [DOI]

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