Skip to main content
SpringerLink
Log in

Approximation Algorithms

  • Chapter
Search Methodologies

Abstract

Most interesting real-world optimization problems are very challenging from a computational point of view. In fact, quite often, finding an optimal or even a near-optimal solution to a large-scale optimization problem may require computational resources far beyond what is practically available. There is a substantial body of literature exploring the computational properties of optimization problems by considering how the computational demands of a solution method grow with the size of the problem instance to be solved (see e.g. Chapter 11 or Aho et al., 1979). A key distinction is made between problems that require computational resources that grow polynomially with problem size versus those for which the required resources grow exponentially. The former category of problems are called efficiently solvable, whereas problems in the latter category are deemed intractable because the exponential growth in required computational resources renders all but the smallest instances of such problems unsolvable.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Agrawal, M., Kayal, N. and Saxena, N., 2002, Primes in P, www.cse.iitk.ac.in/news/primality.html

    Google Scholar 

  • Aho, A. V., Hopcroft, J. E. and Ullman, J. D., 1979, Computers and intractability: A guide to NP-Completeness, Freeman, San Francisco.

    Google Scholar 

  • Aho, A. V., Hopcroft, J. E. and Ullman, J. D., 1983, Data structures and Algorithms, Computer Science and Information Processing Series, Addison-Wesley, Reading, MA

    MATH  Google Scholar 

  • Alon, N. and Spencer, J., 2000, The Probabilistic Method, Wiley, New York

    Book  MATH  Google Scholar 

  • Arora, S., 1998, Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems, J. ACM 45:753–782.

    Article  MATH  MathSciNet  Google Scholar 

  • Arora, S., Lund, C., Motwani, R., Sudan, M. and Szegedy, M., 1998, Proof verification and the hardness of approximation problems, J. ACM 45:501–555.

    Article  MATH  MathSciNet  Google Scholar 

  • Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A. and Protasi, M., 1999, Complexity and Approximation, Springer, Berlin.

    MATH  Google Scholar 

  • Beier, R. and Vocking, B., 2003, Random knapsack in expected polynomial time, Proc. ACM Symp. on Theory of Computing, pp. 232–241.

    Google Scholar 

  • Chazelle, B., 2001, The Discrepancy Method, Cambridge University Press, Cambridge.

    Google Scholar 

  • Chvatal, V., 1979, A greedy heuristic for the set-covering, Math. Oper. Res. 4:233–235.

    Article  MATH  MathSciNet  Google Scholar 

  • Chvatal, V., 1983, Linear Programming, Freeman, San Francisco.

    MATH  Google Scholar 

  • Clay Mathematics Institute, 2003, The millenium prize problems: P vs. NP, http://www.claymath.org/

    Google Scholar 

  • Colbourn, C., 1984, The complexity of completing partial Latin squares, Discrete Appl. Math. 8:25–30.

    Article  MATH  MathSciNet  Google Scholar 

  • Cook, W., Cunningham, W., Pulleyblank, W. and Schrijver, A., 1988, Combinatorial Optimization, Wiley, New York.

    Google Scholar 

  • Cormen, T. H., Leiserson, C. E., Rivest, R. L. and Stein, C, 2001, Introduction to Algorithms, MIT Press, Cambridge, MA.

    MATH  Google Scholar 

  • Dantzig, G., 1998, Linear Programming and Extensions, Princeton University Press, Princeton, NJ.

    MATH  Google Scholar 

  • Feige, U., 2002, Relations between average case complexity and approximation complexity, in: Proc. ACM Symp. on Theory of Computing, pp. 534–543.

    Google Scholar 

  • Feller, W., 1971, An Introduction to Probability Theory and Its Applications, Wiley, New York.

    MATH  Google Scholar 

  • Garey, M. R., Graham, R. L. and Ulman, J. D., 1972, Worst case analysis of memory allocation algorithms, in: Proc. ACM Symp. on Theory of Computing, pp. 143–150.

    Google Scholar 

  • Goemans, M. X. and Williamson, D. P., 1995, Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming, J. ACM 42:1115–1145.

    Article  MATH  MathSciNet  Google Scholar 

  • Goldwasser, S. and Kilian, J., 1986, Almost all primes can be quickly certified, in: Proc. Annual IEEE Symp. on Foundations of Computer Science, pp. 316–329.

    Google Scholar 

  • Gomes, C., Selman, B., Crato, N. and Kautz, H., 2000, Heavy-tailed phenomena in satisfiability and constraint satisfaction problems, J. Autom. Reason. 24:67–100.

    Article  MATH  MathSciNet  Google Scholar 

  • Gomes, C. P., Selman, B. and Kautz, H., 1998, Boosting combinatorial search through randomization, in: Proc. 15th National Conf. on Artificial Intelligence (AAAI-98), AAAI Press, Menlo Park, CA.

    Google Scholar 

  • Gomes, C. P. and Shmoys, D., 2002, The promise of LP to boost CSP techniques for combinatorial problems, in: Proc. 4th Int. Workshop on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimisation Problems (CP-AI-OR’02), Le Croisic, France, N. Jussien and F. Laburthe, eds, pp. 291–305.

    Google Scholar 

  • Graham, R. L., 1966, Bounds for certain multiprocessing anomalies, Bell Syst. Tech. J. 45:1563–1581.

    Google Scholar 

  • Gurevich, Y., 1991, Average Case Complexity, in: Proc. 18th Int. Colloquium on Automata, Languages, and Programming (ICALP’91), Lecture Notes in Computer Science, Vol. 510, pp. 615–628, Springer, Berlin.

    Google Scholar 

  • Hochbaum, D. S., 1997, ed., Approximation Algorithms for NP-Hard Problems, PWS Publishing Company, Boston, MA.

    Google Scholar 

  • Johnson, D. S., 1974, Approximation algorithms for combinatorial problems, J. Comput. Syst. Sci. 9:256–278.

    Article  MATH  Google Scholar 

  • Khot, S. and Regev, O., 2003, Vertex cover might be hard to approximate within 2-e, in: Proc. IEEE Conf. on Computational Complexity.

    Google Scholar 

  • Kirkpatrick, S., Gelatt, C. and Vecchi, M., 1983, Optimization by simulated annealing, Science 220:671–680.

    Article  MathSciNet  Google Scholar 

  • Kozen, D., 1992, The design and analysis of algorithms, Springer, New York.

    Google Scholar 

  • Kumar, S. R., Russell, A. and Sundaram, R., 1999, Approximating Latin square extensions, Algorithmica 24:128–138.

    Article  MATH  MathSciNet  Google Scholar 

  • Laywine, C. and Mullen, G., 1998, Discrete Mathematics using Latin Squares, Discrete Mathematics and Optimization Series, Wiley-Interscience, New York.

    MATH  Google Scholar 

  • Motwani, R. and Raghavan, P., 1995, Randomized Algorithm, Cambridge University Press, Cambridge.

    Google Scholar 

  • Nemhauser, G. and Wolsey, L., 1988, Integer and Combinatorial Optimization, Wiley, New York.

    MATH  Google Scholar 

  • Papadimitriou, C. and Steiglitz, K., 1982, Combinatorial Optimization: Algorithms and Complexity, Prentice-Hall, Englewood Cliffs, NJ.

    MATH  Google Scholar 

  • Rabin, M. (1980). Probabilistic algorithm for testing primality, J. Number Theory 12:128–138.

    Article  MATH  MathSciNet  Google Scholar 

  • Schrijver, A., 2003, Combinatorial Optimization Polyhedra and Efficiency, Springer, Berlin.

    MATH  Google Scholar 

  • Shmoys, D., 1995, Computing near-optimal solutions to combinatorial optimization problems, in: Combinatorial Optimization, Discrete Mathematics and Theoretical Computer Science Series, W. Cook, L. Lovasz and P. Seymour, eds, American Mathematical Society, Providence, RI.

    Google Scholar 

  • Solovay, R. and Strassen, V., 1977, A fast Monte Carlo test for primality, SIAM J. Comput. 6:84–86.

    Article  MATH  MathSciNet  Google Scholar 

  • Srinivasan, A., Approximation algorithms via randomized rounding: a survey. Available from: citeseer.nj.nec.com/493290.html

    Google Scholar 

  • Vazirani, V., 1983, Approximation Algorithms, Springer, Berlin.

    Google Scholar 

  • Williams, R., Gomes, C. P. and Selman, B., 2003, Backdoors to typical case complexity, In Proc. Int. Joint Conf. on Artificial Intelligence (IJCAI).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Cornell University, Ithaca, NY, USA

    Carla P. Gomes

  2. Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA

    Ryan Williams

Authors
  1. Carla P. Gomes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ryan Williams
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Nottingham, UK

    Edmund K. Burke  & Graham Kendall  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Gomes, C.P., Williams, R. (2005). Approximation Algorithms. In: Burke, E.K., Kendall, G. (eds) Search Methodologies. Springer, Boston, MA. https://doi.org/10.1007/0-387-28356-0_18

Download citation

Publish with us

Policies and ethics

Search

Navigation