Dominance Certificates for Combinatorial Optimization Problems

  • Daniel BerendEmail author
  • Steven S. Skiena
  • Yochai Twitto
Part of the Springer Optimization and Its Applications book series (SOIA, volume 139)


Heuristic algorithms, such as simulated annealing, are widely used in practice to solve combinatorial optimization problems. However, they offer no guarantees regarding the quality of the provided solution. An f(I) combinatorial dominance guarantee is a certificate that a solution is not worse than at least f(I) solutions for a particular problem instance I. In this paper, we introduce simple but general techniques for awarding combinatorial dominance certificates to arbitrary solutions of various optimization problems. We demonstrate these techniques by applying them to the Traveling Salesman and Maximum Satisfiability problems, and briefly experiment their usability.



The authors would like to thank Gregory Gutin and the referees for their helpful comments on this paper.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Daniel Berend
    • 1
    • 2
    Email author
  • Steven S. Skiena
    • 3
  • Yochai Twitto
    • 4
  1. 1.Department of Mathematics and of Computer ScienceBen-Gurion UniversityBeer ShevaIsrael
  2. 2.Department of MathematicsRice UniversityHoustonUSA
  3. 3.Department of Computer ScienceStony Brook UniversityStony BrookUSA
  4. 4.Department of Computer ScienceBen-Gurion UniversityBeer ShevaIsrael

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