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On the Hamming distance in combinatorial optimization problems on hypergraph matchings

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Abstract

In this note we consider the properties of the Hamming distance in combinatorial optimization problems on hypergraph matchings, also known as multidimensional assignment problems. It is shown that the Hamming distance between feasible solutions of hypergraph matching problems can be computed as an optimal value of linear assignment problem. For random hypergraph matching problems, an upper bound on the expected Hamming distance to the optimal solution is derived, and an exact expression is obtained in the special case of multidimensional assignment problems with 2 elements in each dimension.

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References

  1. Weinberger E.D.: Correlated and uncorrelated fitness landscapes and how to tell the difference. Biol. Cybern. 63(5), 325–336 (1990)

    Article  MATH  Google Scholar 

  2. Stadler P.F.: Landscapes and their correlation functions. J. Math. Chem. 20(1), 1–45 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  3. Pardalos P.M., Pitsoulis L.: Nonlinear Assignment Problems: Algorithms and Applications. Kluwer, Dordrecht (2000)

    MATH  Google Scholar 

  4. Burkard R.E.: Selected topics on assignment problems. Discret. Appl. Math. 123(1–3), 257–302 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  5. Burkard R.E., Dell’Amico M., Martello S.: Assignment Problems. SIAM, Philadelphia (2009)

    MATH  Google Scholar 

  6. Berge C.: Hypergraphs Combinatorics of Finite Sets. North-Holland, Amsterdam (1989)

    MATH  Google Scholar 

  7. Pierskalla W.: The multidimensional assignment problem. Oper. Res. 16(2), 422–431 (1968)

    Article  MATH  Google Scholar 

  8. Burkard R.E., Çela E.: Linear assignment problems and extensions. In: Du, D.-Z., Pardalos, P.M. (eds) Handbook of Combinatorial Optimization, Supplement Volume A, pp. 75–149. Kluwer, Dordrecht (1999)

    Google Scholar 

  9. Hahn P.M., Kim B.J., Stuetzle T., Kanthak S., Hightower W.L., Samra H., Ding Z., Guignard M.: The quadratic three-dimensional assignment problem Exact and approximate solution methods. Eur. J. Oper. Res. 184(2), 416–428 (2008)

    Article  MATH  Google Scholar 

  10. Hamming R.W.: Error detecting and error correcting codes. Bell Syst. Tech. J. 26(2), 147–160 (1950)

    MathSciNet  Google Scholar 

  11. Matsumoto R., Kurosawa K., Itoh T., Konno T., Uyematsu T.: Primal-dual distance bounds of linear codes with application to cryptography. IEEE Trans. Info. Theory 52(9), 4251–4256 (2006)

    Article  MathSciNet  Google Scholar 

  12. Merz P., Freisleben B.: Fitness landscape analysis and memetic algorithms for the quadratic assignment problem. IEEE Trans. Evol. Comput. 4(4), 337–352 (2000)

    Article  Google Scholar 

  13. Stanley R.: Enumerative Combinatorics. Wadsworth & Brooks, Belmont (1986)

    MATH  Google Scholar 

  14. Jonker R., Volgenant A.: A shortest augmenting path algorithm for dense and sparse linear assignment problems. Computing 38, 325–340 (1987)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. AFRL/RWGN-NRC, 101 West Eglin Blvd, Eglin AFB, FL, 32547, USA

    Alla Kammerdiner

  2. Department of Mechanical and Industrial Engineering, University of Iowa, 3131 Seamans Center, Iowa City, IA, 52242, USA

    Pavlo A. Krokhmal

  3. Department of Industrial and Systems Engineering, Center for Applied Optimization, University of Florida, 303 Weil Hall, Gainesville, FL, 32611, USA

    Panos M. Pardalos

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  1. Alla Kammerdiner
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  2. Pavlo A. Krokhmal
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  3. Panos M. Pardalos
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Correspondence to Pavlo A. Krokhmal.

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Kammerdiner, A., Krokhmal, P.A. & Pardalos, P.M. On the Hamming distance in combinatorial optimization problems on hypergraph matchings. Optim Lett 4, 609–617 (2010). https://doi.org/10.1007/s11590-010-0187-9

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  • DOI: https://doi.org/10.1007/s11590-010-0187-9

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