Combinatorial Search and Heuristic Methods

  • Steven S. Skiena


We can solve many problems to optimality using exhaustive search techniques, although the time complexity can be enormous. For certain applications, it may pay to spend extra time to be certain of the optimal solution. A good example occurs in testing a circuit or a program on all possible inputs. You can prove the correctness of the device by trying all possible inputs and verifying that they give the correct answer. Verifying correctness is a property to be proud of.However, claiming that it works correctly on all the inputs you tried is worth much less.


Local Search Simulated Annealing Solution Space Heuristic Method Partial Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [AK89]
    E. Aarts and J. Korst. Simulated annealing and Boltzman machines: A stochastic approach to combinatorial optimization and neural computing. John Wiley and Sons, 1989.Google Scholar
  2. [AL97]
    E. Aarts and J. K. Lenstra. Local Search in Combinatorial Optimization. John Wiley and Sons, West Sussex, England, 1997.zbMATHGoogle Scholar
  3. [BS97]
    R. Bradley and S. Skiena. Fabricating arrays of strings. In Proc. First Int. Conf. Computational Molecular Biology (RECOMB ’97), pages 57–66, 1997.Google Scholar
  4. [CGJ98]
    C.R. Coullard, A.B. Gamble, and P.C. Jones. Matching problems in selective assembly operations. Annals of Operations Research, 76:95–107, 1998.CrossRefzbMATHGoogle Scholar
  5. [DT04]
    M. Dorigo and T.Stutzle. Ant Colony Optimization. MIT Press, Cambridge MA, 2004.CrossRefzbMATHGoogle Scholar
  6. [DY94]
    Y. Deng and C. Yang. Waring’s problem for pyramidal numbers. Science in China (Series A), 37:377–383, 1994.MathSciNetGoogle Scholar
  7. [FJMO93]
    M. Fredman, D. Johnson, L. McGeoch, and G. Ostheimer. Data structures for traveling salesmen. In Proc. 4th 7th Symp. Discrete Algorithms (SODA), pages 145–154, 1993.Google Scholar
  8. [KGV83]
    S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi. Optimization by simulated annealing. Science, 220:671–680, 1983.CrossRefzbMATHMathSciNetGoogle Scholar
  9. [MF00]
    Z. Michalewicz and D. Fogel. How to Solve it: Modern Heuristics. Springer, Berlin, 2000.zbMATHGoogle Scholar
  10. [Pug86]
    G. Allen Pugh. Partitioning for selective assembly. Computers and Industrial Engineering, 11:175–179, 1986.CrossRefGoogle Scholar
  11. [RHS89]
    A. Robison, B. Hafner, and S. Skiena. Eight pieces cannot cover a chessboard. Computer Journal, 32:567–570, 1989.Google Scholar
  12. [SR03]
    S. Skiena and M. Revilla. Programming Challenges: The Programming Contest Training Manual. Springer-Verlag, 2003.Google Scholar

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.Department of Computer ScienceState University of New York at Stony BrookNew YorkUSA

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