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Concepts of combinatorial optimization [[electronic resource] /] / edited by Vangelis Th. Paschos
| Concepts of combinatorial optimization [[electronic resource] /] / edited by Vangelis Th. Paschos |
| Pubbl/distr/stampa | London, : ISTE |
| Descrizione fisica | 1 online resource (382 p.) |
| Disciplina | 519.64 |
| Altri autori (Persone) | PaschosVangelis Th |
| Collana |
ISTE
Combinatorial optimization |
| Soggetto topico |
Combinatorial optimization
Programming (Mathematics) |
| ISBN |
1-118-60024-X
1-118-60023-1 1-299-18744-7 1-118-60019-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | pt. I. Complexity of combinatorial optimization problems -- pt. II. Classical solution methods -- pt. III. Elements from mathematical programming. |
| Record Nr. | UNINA-9910841642603321 |
| London, : ISTE | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Paradigms of combinatorial optimization : problems and new approaches / / edited by Vangelis Th. Paschos
| Paradigms of combinatorial optimization : problems and new approaches / / edited by Vangelis Th. Paschos |
| Edizione | [Revised and updated second edition.] |
| Pubbl/distr/stampa | London, [England] ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (815 p.) |
| Disciplina | 519.64 |
| Collana | Mathematics and Statistics Series |
| Soggetto topico |
Combinatorial optimization
Programming (Mathematics) |
| ISBN |
1-119-01519-7
1-119-00535-3 1-119-01516-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Copyright; Contents; Preface; PART I: Paradigmatic Problems; Chapter 1: Optimal Satisfiability; 1.1. Introduction; 1.2. Preliminaries; 1.2.1. Constraint satisfaction problems: decision and optimization versions; 1.2.2. Constraint types; 1.3. Complexity of decision problems; 1.4. Complexity and approximation of optimization problems; 1.4.1. Maximization problems; 1.4.2. Minimization problems; 1.5. Particular instances of constraint satisfaction problems; 1.5.1. Planar instances; 1.5.2. Dense instances; 1.5.3. Instances with a bounded number of occurrences
1.6. Satisfiability problems under global constraints 1.7. Conclusion; 1.8. Bibliography; Chapter 2: Scheduling Problems; 2.1. Introduction; 2.2. New techniques for approximation; 2.2.1. Linear programming and scheduling; 2.2.1.1. Single machine problems; 2.2.1.2. Problems with m machines; 2.2.2. An approximation scheme for P||Cmax; 2.3. Constraints and scheduling; 2.3.1. The monomachine constraint; 2.3.2. The cumulative constraint; 2.3.3. Energetic reasoning; 2.4. Non-regular criteria; 2.4.1. PERT with convex costs; 2.4.1.1. The equality graph and its blocks; 2.4.1.2. Generic algorithm 2.4.1.3. Complexity of the generic algorithm 2.4.2. Minimizing the early-tardy cost on one machine; 2.4.2.1. Special cases; 2.4.2.2. The lower bound; 2.4.2.3. The branch-and-bound algorithm; 2.4.2.4. Lower bounds in a node of the search tree; 2.4.2.5. Upper bound; 2.4.2.6. Branching rule; 2.4.2.7. Dominance rules; 2.4.2.8. Experimental results; 2.5. Bibliography; Chapter 3: Location Problems; 3.1. Introduction; 3.1.1. Weber's problem; 3.1.2. A classification; 3.2. Continuous problems; 3.2.1. Complete covering; 3.2.2. Maximal covering; 3.2.2.1. Fixed radius; 3.2.2.2. Variable radius 3.2.3. Empty covering 3.2.4. Bicriteria models; 3.2.5. Covering with multiple resources; 3.3. Discrete problems; 3.3.1. p-Center; 3.3.2. p-Dispersion; 3.3.3. p-Median; 3.3.3.1. Fixed charge; 3.3.4. Hub; 3.3.5. p-Maxisum; 3.4. On-line problems; 3.5. The quadratic assignment problem; 3.5.1. Definitions and formulations of the problem; 3.5.2. Complexity; 3.5.3. Relaxations and lower bounds; 3.5.3.1. Linear relaxations; 3.5.3.2. Semi-definite relaxations; 3.5.3.3. Convex quadratic relaxations; 3.6. Conclusion; 3.7. Bibliography; Chapter 4: Mini Max Algorithms and Games; 4.1. Introduction 4.2. Games of no chance: the simple cases 4.3. The case of complex no chance games; 4.3.1. Approximative evaluation; 4.3.2. Horizon effect; 4.3.3. α-β pruning; 4.4. Quiescence search; 4.4.1. Other refinements of the Mini Max algorithm; 4.5. Case of games using chance; 4.6. Conclusion; 4.7. Bibliography; Chapter 5: Two-dimensional Bin Packing Problems; 5.1. Introduction; 5.2. Models; 5.2.1. ILP models for level packing; 5.3. Upper bounds; 5.3.1. Strip packing; 5.3.2. Bin packing: two-phase heuristics; 5.3.3. Bin packing: one-phase level heuristics 5.3.4. Bin packing: one-phase non-level heuristics |
| Record Nr. | UNINA-9910132156103321 |
| London, [England] ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Paradigms of combinatorial optimization : problems and new approaches / / edited by Vangelis Th. Paschos
| Paradigms of combinatorial optimization : problems and new approaches / / edited by Vangelis Th. Paschos |
| Edizione | [Revised and updated second edition.] |
| Pubbl/distr/stampa | London, [England] ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2014 |
| Descrizione fisica | 1 online resource (815 p.) |
| Disciplina | 519.64 |
| Collana | Mathematics and Statistics Series |
| Soggetto topico |
Combinatorial optimization
Programming (Mathematics) |
| ISBN |
1-119-01519-7
1-119-00535-3 1-119-01516-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Copyright; Contents; Preface; PART I: Paradigmatic Problems; Chapter 1: Optimal Satisfiability; 1.1. Introduction; 1.2. Preliminaries; 1.2.1. Constraint satisfaction problems: decision and optimization versions; 1.2.2. Constraint types; 1.3. Complexity of decision problems; 1.4. Complexity and approximation of optimization problems; 1.4.1. Maximization problems; 1.4.2. Minimization problems; 1.5. Particular instances of constraint satisfaction problems; 1.5.1. Planar instances; 1.5.2. Dense instances; 1.5.3. Instances with a bounded number of occurrences
1.6. Satisfiability problems under global constraints 1.7. Conclusion; 1.8. Bibliography; Chapter 2: Scheduling Problems; 2.1. Introduction; 2.2. New techniques for approximation; 2.2.1. Linear programming and scheduling; 2.2.1.1. Single machine problems; 2.2.1.2. Problems with m machines; 2.2.2. An approximation scheme for P||Cmax; 2.3. Constraints and scheduling; 2.3.1. The monomachine constraint; 2.3.2. The cumulative constraint; 2.3.3. Energetic reasoning; 2.4. Non-regular criteria; 2.4.1. PERT with convex costs; 2.4.1.1. The equality graph and its blocks; 2.4.1.2. Generic algorithm 2.4.1.3. Complexity of the generic algorithm 2.4.2. Minimizing the early-tardy cost on one machine; 2.4.2.1. Special cases; 2.4.2.2. The lower bound; 2.4.2.3. The branch-and-bound algorithm; 2.4.2.4. Lower bounds in a node of the search tree; 2.4.2.5. Upper bound; 2.4.2.6. Branching rule; 2.4.2.7. Dominance rules; 2.4.2.8. Experimental results; 2.5. Bibliography; Chapter 3: Location Problems; 3.1. Introduction; 3.1.1. Weber's problem; 3.1.2. A classification; 3.2. Continuous problems; 3.2.1. Complete covering; 3.2.2. Maximal covering; 3.2.2.1. Fixed radius; 3.2.2.2. Variable radius 3.2.3. Empty covering 3.2.4. Bicriteria models; 3.2.5. Covering with multiple resources; 3.3. Discrete problems; 3.3.1. p-Center; 3.3.2. p-Dispersion; 3.3.3. p-Median; 3.3.3.1. Fixed charge; 3.3.4. Hub; 3.3.5. p-Maxisum; 3.4. On-line problems; 3.5. The quadratic assignment problem; 3.5.1. Definitions and formulations of the problem; 3.5.2. Complexity; 3.5.3. Relaxations and lower bounds; 3.5.3.1. Linear relaxations; 3.5.3.2. Semi-definite relaxations; 3.5.3.3. Convex quadratic relaxations; 3.6. Conclusion; 3.7. Bibliography; Chapter 4: Mini Max Algorithms and Games; 4.1. Introduction 4.2. Games of no chance: the simple cases 4.3. The case of complex no chance games; 4.3.1. Approximative evaluation; 4.3.2. Horizon effect; 4.3.3. α-β pruning; 4.4. Quiescence search; 4.4.1. Other refinements of the Mini Max algorithm; 4.5. Case of games using chance; 4.6. Conclusion; 4.7. Bibliography; Chapter 5: Two-dimensional Bin Packing Problems; 5.1. Introduction; 5.2. Models; 5.2.1. ILP models for level packing; 5.3. Upper bounds; 5.3.1. Strip packing; 5.3.2. Bin packing: two-phase heuristics; 5.3.3. Bin packing: one-phase level heuristics 5.3.4. Bin packing: one-phase non-level heuristics |
| Record Nr. | UNINA-9910808645503321 |
| London, [England] ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Probabilistic combinatorial optimization on graphs [[electronic resource] /] / Cécile Murat and Vangelis Th. Paschos
| Probabilistic combinatorial optimization on graphs [[electronic resource] /] / Cécile Murat and Vangelis Th. Paschos |
| Autore | Murat Cecile |
| Pubbl/distr/stampa | London ; ; Newport Beach, CA, : ISTE, 2006 |
| Descrizione fisica | 1 online resource (269 p.) |
| Disciplina |
511.6
519.2 |
| Altri autori (Persone) | PaschosVangelis Th |
| Collana | ISTE |
| Soggetto topico |
Combinatorial probabilities
Combinatorial optimization Random graphs |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-51061-7
9786610510610 1-84704-483-2 0-470-39464-1 0-470-61250-9 1-84704-583-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Probabilistic Combinatorial Optimization on Graphs; Contents; Preface; Chapter 1. A Short Insight into Probabilistic Combinatorial Optimization; 1.1. Motivations and applications; 1.2. A formalism for probabilistic combinatorial optimization; 1.3. The main methodological issues dealing with probabilistic combinatorial optimization; 1.3.1. Complexity issues; 1.3.1.1. Membership in NPO is not always obvious; 1.3.1.2. Complexity of deterministic vs. complexity of probabilistic optimization problems; 1.3.2. Solution issues; 1.3.2.1. Characterization of optimal a priori solutions
1.3.2.2. Polynomial subcases1.3.2.3. Exact solutions and polynomial approximation issues; 1.4. Miscellaneous and bibliographic notes; First Part. Probabilistic Graph-Problems; Chapter 2. The Probabilistic Maximum Independent Set; 2.1. The modification strategies and a preliminary result; 2.1.1. Strategy M1; 2.1.2. Strategies M2 and M3; 2.1.3. Strategy M4; 2.1.4. Strategy M5; 2.1.5. A general mathematical formulation for the five functionals; 2.2. PROBABILISTIC MAX INDEPENDENT SET1; 2.2.1. Computing optimal a priori solutions; 2.2.2. Approximating optimal solutions 2.2.3. Dealing with bipartite graphs2.3. PROBABILISTIC MAX INDEPENDENT SET2 and 3; 2.3.1. Expressions for E(G, S, M2) and E(G, S, M3); 2.3.2. An upper bound for the complexity of E(G, S, M2); 2.3.3. Bounds for E(G, S, M2); 2.3.4. Approximating optimal solutions; 2.3.4.1. Using argmax {ΣviESpi} as an a priori solution; 2.3.4.2. Using approximations of MAX INDEPENDENT SET; 2.3.5. Dealing with bipartite graphs; 2.4. PROBABILISTIC MAX INDEPENDENT SET4; 2.4.1. An expression for E(G, S, M4); 2.4.2. Using S* or argmax{ΣviESpi} as an a priori solution; 2.4.3. Dealing with bipartite graphs 2.5. PROBABILISTIC MAX INDEPENDENT SET52.5.1. In general graphs; 2.5.2. In bipartite graphs; 2.6. Summary of the results; 2.7. Methodological questions; 2.7.1. Maximizing a criterion associated with gain; 2.7.1.1. The minimum gain criterion; 2.7.1.2. The maximum gain criterion; 2.7.2. Minimizing a criterion associated with regret; 2.7.2.1. The maximum regret criterion; 2.7.3. Optimizing expectation; 2.8. Proofs of the results; 2.8.1. Proof of Proposition 2.1; 2.8.2. Proof of Theorem 2.6; 2.8.3. Proof of Proposition 2.3; 2.8.4. Proof of Theorem 2.13 Chapter 3. The Probabilistic Minimum Vertex Cover3.1. The strategies M1, M2 and M3 and a general preliminary result; 3.1.1. Specification of M1, M2 and M3; 3.1.1.1. Strategy M1; 3.1.1.2. Strategy M2; 3.1.1.3. Strategy M3; 3.1.2. A first expression for the functionals; 3.2. PROBABILISTIC MIN VERTEX COVER1; 3.3. PROBABILISTIC MIN VERTEX COVER2; 3.4. PROBABILISTIC MIN VERTEX COVER3; 3.4.1. Building E(G, C, M3); 3.4.2. Bounds for E(G, C, M3); 3.5. Some methodological questions; 3.6. Proofs of the results; 3.6.1. Proof of Theorem 3.3; 3.6.2. On the the bounds obtained in Theorem 3.3 Chapter 4. The Probabilistic Longest Path |
| Record Nr. | UNINA-9910143315903321 |
Murat Cecile
|
||
| London ; ; Newport Beach, CA, : ISTE, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Probabilistic combinatorial optimization on graphs [[electronic resource] /] / Cécile Murat and Vangelis Th. Paschos
| Probabilistic combinatorial optimization on graphs [[electronic resource] /] / Cécile Murat and Vangelis Th. Paschos |
| Autore | Murat Cecile |
| Pubbl/distr/stampa | London ; ; Newport Beach, CA, : ISTE, 2006 |
| Descrizione fisica | 1 online resource (269 p.) |
| Disciplina |
511.6
519.2 |
| Altri autori (Persone) | PaschosVangelis Th |
| Collana | ISTE |
| Soggetto topico |
Combinatorial probabilities
Combinatorial optimization Random graphs |
| ISBN |
1-280-51061-7
9786610510610 1-84704-483-2 0-470-39464-1 0-470-61250-9 1-84704-583-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Probabilistic Combinatorial Optimization on Graphs; Contents; Preface; Chapter 1. A Short Insight into Probabilistic Combinatorial Optimization; 1.1. Motivations and applications; 1.2. A formalism for probabilistic combinatorial optimization; 1.3. The main methodological issues dealing with probabilistic combinatorial optimization; 1.3.1. Complexity issues; 1.3.1.1. Membership in NPO is not always obvious; 1.3.1.2. Complexity of deterministic vs. complexity of probabilistic optimization problems; 1.3.2. Solution issues; 1.3.2.1. Characterization of optimal a priori solutions
1.3.2.2. Polynomial subcases1.3.2.3. Exact solutions and polynomial approximation issues; 1.4. Miscellaneous and bibliographic notes; First Part. Probabilistic Graph-Problems; Chapter 2. The Probabilistic Maximum Independent Set; 2.1. The modification strategies and a preliminary result; 2.1.1. Strategy M1; 2.1.2. Strategies M2 and M3; 2.1.3. Strategy M4; 2.1.4. Strategy M5; 2.1.5. A general mathematical formulation for the five functionals; 2.2. PROBABILISTIC MAX INDEPENDENT SET1; 2.2.1. Computing optimal a priori solutions; 2.2.2. Approximating optimal solutions 2.2.3. Dealing with bipartite graphs2.3. PROBABILISTIC MAX INDEPENDENT SET2 and 3; 2.3.1. Expressions for E(G, S, M2) and E(G, S, M3); 2.3.2. An upper bound for the complexity of E(G, S, M2); 2.3.3. Bounds for E(G, S, M2); 2.3.4. Approximating optimal solutions; 2.3.4.1. Using argmax {ΣviESpi} as an a priori solution; 2.3.4.2. Using approximations of MAX INDEPENDENT SET; 2.3.5. Dealing with bipartite graphs; 2.4. PROBABILISTIC MAX INDEPENDENT SET4; 2.4.1. An expression for E(G, S, M4); 2.4.2. Using S* or argmax{ΣviESpi} as an a priori solution; 2.4.3. Dealing with bipartite graphs 2.5. PROBABILISTIC MAX INDEPENDENT SET52.5.1. In general graphs; 2.5.2. In bipartite graphs; 2.6. Summary of the results; 2.7. Methodological questions; 2.7.1. Maximizing a criterion associated with gain; 2.7.1.1. The minimum gain criterion; 2.7.1.2. The maximum gain criterion; 2.7.2. Minimizing a criterion associated with regret; 2.7.2.1. The maximum regret criterion; 2.7.3. Optimizing expectation; 2.8. Proofs of the results; 2.8.1. Proof of Proposition 2.1; 2.8.2. Proof of Theorem 2.6; 2.8.3. Proof of Proposition 2.3; 2.8.4. Proof of Theorem 2.13 Chapter 3. The Probabilistic Minimum Vertex Cover3.1. The strategies M1, M2 and M3 and a general preliminary result; 3.1.1. Specification of M1, M2 and M3; 3.1.1.1. Strategy M1; 3.1.1.2. Strategy M2; 3.1.1.3. Strategy M3; 3.1.2. A first expression for the functionals; 3.2. PROBABILISTIC MIN VERTEX COVER1; 3.3. PROBABILISTIC MIN VERTEX COVER2; 3.4. PROBABILISTIC MIN VERTEX COVER3; 3.4.1. Building E(G, C, M3); 3.4.2. Bounds for E(G, C, M3); 3.5. Some methodological questions; 3.6. Proofs of the results; 3.6.1. Proof of Theorem 3.3; 3.6.2. On the the bounds obtained in Theorem 3.3 Chapter 4. The Probabilistic Longest Path |
| Record Nr. | UNISA-996216942703316 |
|
Murat Cecile
|
||
| London ; ; Newport Beach, CA, : ISTE, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Probabilistic combinatorial optimization on graphs [[electronic resource] /] / Cécile Murat and Vangelis Th. Paschos
| Probabilistic combinatorial optimization on graphs [[electronic resource] /] / Cécile Murat and Vangelis Th. Paschos |
| Autore | Murat Cecile |
| Pubbl/distr/stampa | London ; ; Newport Beach, CA, : ISTE, 2006 |
| Descrizione fisica | 1 online resource (269 p.) |
| Disciplina |
511.6
519.2 |
| Altri autori (Persone) | PaschosVangelis Th |
| Collana | ISTE |
| Soggetto topico |
Combinatorial probabilities
Combinatorial optimization Random graphs |
| ISBN |
1-280-51061-7
9786610510610 1-84704-483-2 0-470-39464-1 0-470-61250-9 1-84704-583-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Probabilistic Combinatorial Optimization on Graphs; Contents; Preface; Chapter 1. A Short Insight into Probabilistic Combinatorial Optimization; 1.1. Motivations and applications; 1.2. A formalism for probabilistic combinatorial optimization; 1.3. The main methodological issues dealing with probabilistic combinatorial optimization; 1.3.1. Complexity issues; 1.3.1.1. Membership in NPO is not always obvious; 1.3.1.2. Complexity of deterministic vs. complexity of probabilistic optimization problems; 1.3.2. Solution issues; 1.3.2.1. Characterization of optimal a priori solutions
1.3.2.2. Polynomial subcases1.3.2.3. Exact solutions and polynomial approximation issues; 1.4. Miscellaneous and bibliographic notes; First Part. Probabilistic Graph-Problems; Chapter 2. The Probabilistic Maximum Independent Set; 2.1. The modification strategies and a preliminary result; 2.1.1. Strategy M1; 2.1.2. Strategies M2 and M3; 2.1.3. Strategy M4; 2.1.4. Strategy M5; 2.1.5. A general mathematical formulation for the five functionals; 2.2. PROBABILISTIC MAX INDEPENDENT SET1; 2.2.1. Computing optimal a priori solutions; 2.2.2. Approximating optimal solutions 2.2.3. Dealing with bipartite graphs2.3. PROBABILISTIC MAX INDEPENDENT SET2 and 3; 2.3.1. Expressions for E(G, S, M2) and E(G, S, M3); 2.3.2. An upper bound for the complexity of E(G, S, M2); 2.3.3. Bounds for E(G, S, M2); 2.3.4. Approximating optimal solutions; 2.3.4.1. Using argmax {ΣviESpi} as an a priori solution; 2.3.4.2. Using approximations of MAX INDEPENDENT SET; 2.3.5. Dealing with bipartite graphs; 2.4. PROBABILISTIC MAX INDEPENDENT SET4; 2.4.1. An expression for E(G, S, M4); 2.4.2. Using S* or argmax{ΣviESpi} as an a priori solution; 2.4.3. Dealing with bipartite graphs 2.5. PROBABILISTIC MAX INDEPENDENT SET52.5.1. In general graphs; 2.5.2. In bipartite graphs; 2.6. Summary of the results; 2.7. Methodological questions; 2.7.1. Maximizing a criterion associated with gain; 2.7.1.1. The minimum gain criterion; 2.7.1.2. The maximum gain criterion; 2.7.2. Minimizing a criterion associated with regret; 2.7.2.1. The maximum regret criterion; 2.7.3. Optimizing expectation; 2.8. Proofs of the results; 2.8.1. Proof of Proposition 2.1; 2.8.2. Proof of Theorem 2.6; 2.8.3. Proof of Proposition 2.3; 2.8.4. Proof of Theorem 2.13 Chapter 3. The Probabilistic Minimum Vertex Cover3.1. The strategies M1, M2 and M3 and a general preliminary result; 3.1.1. Specification of M1, M2 and M3; 3.1.1.1. Strategy M1; 3.1.1.2. Strategy M2; 3.1.1.3. Strategy M3; 3.1.2. A first expression for the functionals; 3.2. PROBABILISTIC MIN VERTEX COVER1; 3.3. PROBABILISTIC MIN VERTEX COVER2; 3.4. PROBABILISTIC MIN VERTEX COVER3; 3.4.1. Building E(G, C, M3); 3.4.2. Bounds for E(G, C, M3); 3.5. Some methodological questions; 3.6. Proofs of the results; 3.6.1. Proof of Theorem 3.3; 3.6.2. On the the bounds obtained in Theorem 3.3 Chapter 4. The Probabilistic Longest Path |
| Record Nr. | UNINA-9910830041603321 |
|
Murat Cecile
|
||
| London ; ; Newport Beach, CA, : ISTE, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Probabilistic combinatorial optimization on graphs [[electronic resource] /] / Cécile Murat and Vangelis Th. Paschos
| Probabilistic combinatorial optimization on graphs [[electronic resource] /] / Cécile Murat and Vangelis Th. Paschos |
| Autore | Murat Cecile |
| Pubbl/distr/stampa | London ; ; Newport Beach, CA, : ISTE, 2006 |
| Descrizione fisica | 1 online resource (269 p.) |
| Disciplina |
511.6
519.2 |
| Altri autori (Persone) | PaschosVangelis Th |
| Collana | ISTE |
| Soggetto topico |
Combinatorial probabilities
Combinatorial optimization Random graphs |
| ISBN |
1-280-51061-7
9786610510610 1-84704-483-2 0-470-39464-1 0-470-61250-9 1-84704-583-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Probabilistic Combinatorial Optimization on Graphs; Contents; Preface; Chapter 1. A Short Insight into Probabilistic Combinatorial Optimization; 1.1. Motivations and applications; 1.2. A formalism for probabilistic combinatorial optimization; 1.3. The main methodological issues dealing with probabilistic combinatorial optimization; 1.3.1. Complexity issues; 1.3.1.1. Membership in NPO is not always obvious; 1.3.1.2. Complexity of deterministic vs. complexity of probabilistic optimization problems; 1.3.2. Solution issues; 1.3.2.1. Characterization of optimal a priori solutions
1.3.2.2. Polynomial subcases1.3.2.3. Exact solutions and polynomial approximation issues; 1.4. Miscellaneous and bibliographic notes; First Part. Probabilistic Graph-Problems; Chapter 2. The Probabilistic Maximum Independent Set; 2.1. The modification strategies and a preliminary result; 2.1.1. Strategy M1; 2.1.2. Strategies M2 and M3; 2.1.3. Strategy M4; 2.1.4. Strategy M5; 2.1.5. A general mathematical formulation for the five functionals; 2.2. PROBABILISTIC MAX INDEPENDENT SET1; 2.2.1. Computing optimal a priori solutions; 2.2.2. Approximating optimal solutions 2.2.3. Dealing with bipartite graphs2.3. PROBABILISTIC MAX INDEPENDENT SET2 and 3; 2.3.1. Expressions for E(G, S, M2) and E(G, S, M3); 2.3.2. An upper bound for the complexity of E(G, S, M2); 2.3.3. Bounds for E(G, S, M2); 2.3.4. Approximating optimal solutions; 2.3.4.1. Using argmax {ΣviESpi} as an a priori solution; 2.3.4.2. Using approximations of MAX INDEPENDENT SET; 2.3.5. Dealing with bipartite graphs; 2.4. PROBABILISTIC MAX INDEPENDENT SET4; 2.4.1. An expression for E(G, S, M4); 2.4.2. Using S* or argmax{ΣviESpi} as an a priori solution; 2.4.3. Dealing with bipartite graphs 2.5. PROBABILISTIC MAX INDEPENDENT SET52.5.1. In general graphs; 2.5.2. In bipartite graphs; 2.6. Summary of the results; 2.7. Methodological questions; 2.7.1. Maximizing a criterion associated with gain; 2.7.1.1. The minimum gain criterion; 2.7.1.2. The maximum gain criterion; 2.7.2. Minimizing a criterion associated with regret; 2.7.2.1. The maximum regret criterion; 2.7.3. Optimizing expectation; 2.8. Proofs of the results; 2.8.1. Proof of Proposition 2.1; 2.8.2. Proof of Theorem 2.6; 2.8.3. Proof of Proposition 2.3; 2.8.4. Proof of Theorem 2.13 Chapter 3. The Probabilistic Minimum Vertex Cover3.1. The strategies M1, M2 and M3 and a general preliminary result; 3.1.1. Specification of M1, M2 and M3; 3.1.1.1. Strategy M1; 3.1.1.2. Strategy M2; 3.1.1.3. Strategy M3; 3.1.2. A first expression for the functionals; 3.2. PROBABILISTIC MIN VERTEX COVER1; 3.3. PROBABILISTIC MIN VERTEX COVER2; 3.4. PROBABILISTIC MIN VERTEX COVER3; 3.4.1. Building E(G, C, M3); 3.4.2. Bounds for E(G, C, M3); 3.5. Some methodological questions; 3.6. Proofs of the results; 3.6.1. Proof of Theorem 3.3; 3.6.2. On the the bounds obtained in Theorem 3.3 Chapter 4. The Probabilistic Longest Path |
| Record Nr. | UNINA-9910841663103321 |
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Murat Cecile
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| London ; ; Newport Beach, CA, : ISTE, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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