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Optimization problems in graph theory : in honor of Gregory Z. Gutin's 60th birthday

Author: Boris Goldengorin; Gregory Gutin
Publisher: Cham, Switzerland : Springer, [2018]
Series: Springer optimization and its applications, v. 139.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book presents open optimization problems in graph theory and networks. Each chapter reflects developments in theory and applications based on Gregory Gutin's fundamental contributions to advanced methods and techniques in combinatorial optimization. Researchers, students, and engineers in computer science, big data, applied mathematics, operations research, algorithm design, artificial intelligence, software  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Boris Goldengorin; Gregory Gutin
ISBN: 9783319948300 331994830X 9783319948317 3319948318
OCLC Number: 1055160512
Description: 1 online resource.
Contents: Intro; Preface; Acknowledgements; Contents; Dr. Gregory Gutin --
Short Bio; Gregory Gutin and Graph Optimization Problems; On Graphs Whose Maximal Cliques and Stable Sets Intersect; 1 Introduction; 1.1 CIS-Graphs and Simplicial Vertices; 1.2 Almost CIS-Graphs and Split Graphs; 1.3 P4-Free CIS-Graphs; 1.4 Combs and Anti-combs; 1.5 (n, k,)-Graphs and Their Complements; 1.6 Gallai's and CIS-d-Graphs; 1.7 Extending Cameron-Edmonds-Lovász' Theorem; 1.8 On families of Graphs Closed with Respect to Substitution; 1.9 Almost CIS-d-Graphs; 2 Proof of Theorem 2; 2.1 Plan of the Proof of Theorem 2. 4.1 A Quadratically Constrained Quadratic Programming Model4.2 An Unconstrained Binary Quadratic Programming Model; 4.3 The 0/1 Linear Model; 4.4 Additional Constraints for the 0/1 Linear Model; 5 Numerical Results in Random Graphs; 5.1 Performance of the 0/1 Linear Model on Random Graphs; 5.2 Impact of Negative Edges on the Frustration Index; 5.3 Impact of Graph Size and Density on the Frustration Index; 6 Numerical Results in Real Signed Networks; 7 Conclusion and Future Research; References; Optimal Factorization of Operators by Operators That Are Consistent with the Graph's Structure. 1 General Factorization Problem Statement2 Factorization of Linear Operators; 3 The Upper Bound of the Factorization Depth; 4 Conclusion; References; Branching in Digraphs with Many and Few Leaves: Structural and Algorithmic Results; 1 Introduction; 2 Terminology, Notation, and Preliminaries; 3 Minimum Leaf Out-Branchings; 3.1 Upper Bounds on min(D); 3.2 Acyclic Digraphs; 3.3 FPT Algorithms for General Digraphs; 4 Maximum Leaf Out-Branchings; References; Dominance Certificates for Combinatorial Optimization Problems; 1 Introduction; 1.1 Previous Work; 1.2 Definitions. 2 Certified Dominance Bounds for Arbitrary Solutions2.1 TSP Certification; 2.2 MaxSat Certification; 2.3 A Confidence Interval for the Blackball Ratio; 3 Experimental Results; 3.1 Results on the Chebyshev's Bound-Based Technique; 3.2 Results on the Confidence Interval-Based Technique; 4 Discussion; References; Conditional Markov Chain Search for the Simple Plant Location Problem Improves Upper Bounds on Twelve Körkel-Ghosh Instances; 1 Introduction; 2 SPLP Components; 2.1 Data Structures; 2.2 Open Random (k); 2.3 Close Random (k); 2.4 Open Best; 2.5 Close Best; 2.6 Exchange Best.
Series Title: Springer optimization and its applications, v. 139.
Responsibility: Boris Goldengorin, editor.

Abstract:

This book presents open optimization problems in graph theory and networks. Each chapter reflects developments in theory and applications based on Gregory Gutin's fundamental contributions to advanced methods and techniques in combinatorial optimization. Researchers, students, and engineers in computer science, big data, applied mathematics, operations research, algorithm design, artificial intelligence, software engineering, data analysis, industrial and systems engineering will benefit from the state-of-the-art results presented in modern graph theory and its applications to the design of efficient algorithms for optimization problems. Topics covered in this work include: · Algorithmic aspects of problems with disjoint cycles in graphs · Graphs where maximal cliques and stable sets intersect · The maximum independent set problem with special classes · A general technique for heuristic algorithms for optimization problems · The network design problem with cut constraints · Algorithms for computing the frustration index of a signed graph · A heuristic approach for studying the patrol problem on a graph · Minimum possible sum and product of the proper connection number · Structural and algorithmic results on branchings in digraphs · Improved upper bounds for Korkel--Ghosh benchmark SPLP instances.--

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