Advertisement

Complexity and Approximation

Combinatorial Optimization Problems and Their Approximability Properties

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

Table of contents

  1. Front Matter
    Pages i-xix
  2. Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann
    Pages 1-37
  3. Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann
    Pages 39-85
  4. Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann
    Pages 87-122
  5. Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann
    Pages 123-151
  6. Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann
    Pages 153-174
  7. Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann
    Pages 175-205
  8. Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann
    Pages 207-251
  9. Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann
    Pages 253-286
  10. Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann
    Pages 287-320
  11. Giorgio Ausiello, Alberto Marchetti-Spaccamela, Pierluigi Crescenzi, Giorgio Gambosi, Marco Protasi, Viggo Kann
    Pages 321-351
  12. Back Matter
    Pages 353-524

About this book

Introduction

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.

Keywords

Approximation Combinatorial Algorithms Complexity Computer Partition Scheduling Variable calculus combinatorial optimization complexity theory genetic algorithms linear optimization logic optimization programming

Authors and affiliations

  • Giorgio Ausiello
    • 1
  • Alberto Marchetti-Spaccamela
    • 1
  • Pierluigi Crescenzi
    • 2
  • Giorgio Gambosi
    • 3
  • Marco Protasi
    • 3
  • Viggo Kann
    • 4
  1. 1.Dipartimento di Informatica e SistemisticaUniversità di Roma “La Sapienza”RomeItaly
  2. 2.Dipartimento di Sistemi e InformaticaUniversità degli Studi di FirenzeFlorenceItaly
  3. 3.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomeItaly
  4. 4.NADA, Department of Numerical Analysis and Computing ScienceKTH, Royal Institute of TechnologyStockholmSweden

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-58412-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-63581-6
  • Online ISBN 978-3-642-58412-1
  • Buy this book on publisher's site