Cybernetics and Systems Analysis

, Volume 46, Issue 6, pp 879–883 | Cite as

Reoptimization of set covering problems

Article

Abstract

If an element is inserted into or removed from a set, then the set covering problem can be reoptimized with some ratio \( \left( {2 - \frac{1}{{\ln m + 1}}} \right) \), where m is the number of elements of the set. A similar result holds if an arbitrary number 1 < p < m of elements of the set is inserted or removed.

Keywords

reoptimization r-approximation algorithm 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. Ausiello, B. Escoffier, J. Monnot, and V. Th. Paschos, “Reoptimization of minimum and maximum traveling salesman’s tours,” in: Proc. SWAT 2006; LNCS, 4059, 196–207, Springer, Berlin (2006).Google Scholar
  2. 2.
    H. J. Bockenhauer, L. Forlizzi, J. Hromkovic, et al., “On the approximability of TSP on local modifications of optimal solved instances,” Algorithmic Oper. Res., 2(2), 83–93 (2007).MathSciNetGoogle Scholar
  3. 3.
    H. J. Bockenhauer, J. Hromkovic, T. Momke, and P. Widmayer, “On the hardness of reoptimization,” in: Proc. 34th Intern. Conf. on Current Trends in Theory and Practice of Computer Science (SOF-SEM 2008); LNCS, 4910, 50–65, Springer, Berlin (2008)Google Scholar
  4. 4.
    B. Escoffier, M. Milanic, and V. Th. Paschos, “Simple and fast reoptimizations for the Steiner tree problem,” Algorithmic Oper. Res., 4(2), 86–94 (2009).MathSciNetGoogle Scholar
  5. 5.
    C. Archetti, L. Bertazzi, and M. G. Speranza, “Reoptimizing the traveling salesman problem,” Networks, 42(3), 154–159 (2003).MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    C. Archetti, L. Bertazzi, and M. G. Speranza, “Reoptimizing the 0-1 knapsack problem,” Manuscript (2008).Google Scholar
  7. 7.
    G. Ausiello, V. Bonifaci, and B. Escoffier, “Complexity and approximation in reoptimization,” in: Computability in Context: Computation and Logic in the Real World, Computability in Europe (CiE) Conference 2007 (June, 2007), Imperial College Press (2010), pp. 24–33.Google Scholar
  8. 8.
    V. A. Chvatal, “A greedy heuristic for the set covering problem,” Math. Oper. Res., 4, No. 3, 233–235 (1979).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine

Personalised recommendations