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Reoptimization of set covering problems

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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.

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References

  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. 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).

    MathSciNet  Google Scholar 

  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. 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).

    MathSciNet  Google Scholar 

  5. C. Archetti, L. Bertazzi, and M. G. Speranza, “Reoptimizing the traveling salesman problem,” Networks, 42(3), 154–159 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  6. C. Archetti, L. Bertazzi, and M. G. Speranza, “Reoptimizing the 0-1 knapsack problem,” Manuscript (2008).

  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.

  8. V. A. Chvatal, “A greedy heuristic for the set covering problem,” Math. Oper. Res., 4, No. 3, 233–235 (1979).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    V. A. Mikhailyuk

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  1. V. A. Mikhailyuk
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Correspondence to V. A. Mikhailyuk.

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Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 27–31, November–December 2010.

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Mikhailyuk, V.A. Reoptimization of set covering problems. Cybern Syst Anal 46, 879–883 (2010). https://doi.org/10.1007/s10559-010-9269-z

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