Complexity and Approximation

1. Front Matter

   Pages i-xix

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2. The Complexity of Optimization Problems

   • Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann

   Pages 1-37

3. Design Techniques for Approximation Algorithms

   • Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann

   Pages 39-85

4. Approximation Classes

   • Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann

   Pages 87-122

5. Input-Dependent and Asymptotic Approximation

   • Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann

   Pages 123-151

6. Approximation through Randomization

   • Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann

   Pages 153-174

7. NP, PCP and Non-approximability Results

   • Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann

   Pages 175-205

8. The PCP theorem

   • Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann

   Pages 207-251

9. Approximation Preserving Reductions

   • Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann

   Pages 253-286

10. Probabilistic analysis of approximation algorithms

    • Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann

    Pages 287-320

11. Heuristic methods

    • Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann

    Pages 321-351

12. Back Matter

    Pages 353-524

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N COMPUTER applications we are used to live with approximation. Var­ I ious notions of approximation appear, in fact, in many circumstances. One notable example is the type of approximation that arises in numer­ ical analysis or in computational geometry from the fact that we cannot perform computations with arbitrary precision and we have to truncate the representation of real numbers. In other cases, we use to approximate com­ plex mathematical objects by simpler ones: for example, we sometimes represent non-linear functions by means of piecewise linear ones. The need to solve difficult optimization problems is another reason that forces us to deal with approximation. In particular, when a problem is computationally hard (i. e. , the only way we know to solve it is by making use of an algorithm that runs in exponential time), it may be practically unfeasible to try to compute the exact solution, because it might require months or years of machine time, even with the help of powerful parallel computers. In such cases, we may decide to restrict ourselves to compute a solution that, though not being an optimal one, nevertheless is close to the optimum and may be determined in polynomial time. We call this type of solution an approximate solution and the corresponding algorithm a polynomial-time approximation algorithm. Most combinatorial optimization problems of great practical relevance are, indeed, computationally intractable in the above sense. In formal terms, they are classified as Np-hard optimization problems.

• Approximation
• Combinatorial Algorithms
• Complexity
• Computer
• Partition
• Scheduling
• Variable
• calculus
• combinatorial optimization
• complexity theory
• genetic algorithms
• linear optimization
• logic
• optimization
• programming
• algorithm analysis and problem complexity

• Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, Rome, Italy

  Giorgio Ausiello, Alberto Marchetti-Spaccamela

• Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze, Florence, Italy

  Pierluigi Crescenzi

• Dipartimento di Matematica, Università di Roma “Tor Vergata”, Rome, Italy

  Giorgio Gambosi, Marco Protasi

• NADA, Department of Numerical Analysis and Computing Science, KTH, Royal Institute of Technology, Stockholm, Sweden

  Viggo Kann

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