Concepts of combinatorial optimization /
Combinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes of the Combinatorial Optimization series aim to cover a wide range of topics in this area. These to...
| Άλλοι συγγραφείς: | |
|---|---|
| Μορφή: | Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
Hoboken :
Wiley,
2014.
|
| Έκδοση: | 2nd ed. |
| Σειρά: | ISTE.
|
| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- Cover; Title Page; Copyright; Contents; Preface; PART I: Complexity of CombinatorialOptimization Problems; Chapter 1: Basic Concepts in Algorithmsand Complexity Theory; 1.1. Algorithmic complexity; 1.2. Problem complexity; 1.3. The classes P, NP and NPO; 1.4. Karp and Turing reductions; 1.5. NP-completeness; 1.6. Two examples of NP-complete problems; 1.6.1. MIN VERTEX COVER; 1.6.2. MAX STABLE; 1.7. A few words on strong and weak NP-completeness; 1.8. A few other well-known complexity classes; 1.9. Bibliography; Chapter 2: Randomized Complexity; 2.1. Deterministic and probabilistic algorithms.
- 2.1.1. Complexity of a Las Vegas algorithm2.1.2. Probabilistic complexity of a problem; 2.2. Lower bound technique; 2.2.1. Definitions and notations; 2.2.2. Minimax theorem; 2.2.3. The Loomis lemma and the Yao principle; 2.3. Elementary intersection problem; 2.3.1. Upper bound; 2.3.2. Lower bound; 2.3.3. Probabilistic complexity; 2.4. Conclusion; 2.5. Bibliography; PART II: Classical Solution Methods; Chapter 3: Branch-and-Bound Methods; 3.1. Introduction; 3.2. Branch-and-bound method principles; 3.2.1. Principle of separation; 3.2.2. Pruning principles; 3.2.2.1. Bound.
- 3.2.2.2. Evaluation function3.2.2.3. Use of the bound and of the evaluation function for pruning; 3.2.2.4. Other pruning principles; 3.2.2.5. Pruning order; 3.2.3. Developing the tree; 3.2.3.1. Description of development strategies; 3.2.3.2. Compared properties of the depth first and best first strategies; 3.3. A detailed example: the binary knapsack problem; 3.3.1. Calculating the initial bound; 3.3.2. First principle of separation; 3.3.3. Pruning without evaluation; 3.3.4. Evaluation; 3.3.5. Complete execution of the branch-and-bound method for finding only oneoptimal solution.
- 3.3.6. First variant: finding all the optimal solutions3.3.7. Second variant: best first search strategy; 3.3.8. Third variant: second principle of separation; 3.4. Conclusion; 3.5. Bibliography; Chapter 4: Dynamic Programming; 4.1. Introduction; 4.2. A first example: crossing the bridge; 4.3. Formalization; 4.3.1. State space, decision set, transition function; 4.3.2. Feasible policies, comparison relationships and objectives; 4.4. Some other examples; 4.4.1. Stock management; 4.4.2. Shortest path bottleneck in a graph; 4.4.3. Knapsack problem; 4.5. Solution; 4.5.1. Forward procedure.
- 4.5.2. Backward procedure4.5.3. Principles of optimality and monotonicity; 4.6. Solution of the examples; 4.6.1. Stock management; 4.6.2. Shortest path bottleneck; 4.6.3. Knapsack; 4.7. A few extensions; 4.7.1. Partial order and multicriteria optimization; 4.7.1.1. New formulation of the problem; 4.7.1.2. Solution; 4.7.1.3. Examples; 4.7.2. Dynamic programming with variables; 4.7.2.1. Sequential decision problems under uncertainty; 4.7.2.2. Solution; 4.7.2.3. Example; 4.7.3. Generalized dynamic programming; 4.8. Conclusion; 4.9. Bibliography; PART III: Elements from MathematicalProgramming.
