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On limitations of transformations between combinatorial problems

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Abstract

We define a class of “local transformations” that includes many transformations from the NP-completeness literature. We then prove (without assuming P≠NP) that this type of transformation is too weak to transform 3SAT or a number of other NP-complete problems into 2SAT or a number of other problems in P. The proof uses concepts related to distributed computing.

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References

  • Garey, M. R., and Johnson, D. S. (1979),Computers and Intractability: A Guide to the Theory of NP-Completeness, Prentice-Hall, Englewood Cliffs, NJ.

    Google Scholar 

  • Garey, M. R., Johnson, D. S., and Stockmeyer, L. (1976), Some simplified NP-complete graph problems,Theoret. Comput. Sci. 1, 237–267.

    Google Scholar 

  • Hopcroft, J. E., and Ullman, J. D. (1979),Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, MA.

    Google Scholar 

  • Karp, R. M. (1972), Reducibility among combinatorial problems, inComplexity of Computer Computations (R. E. Miller and J. W. Thatcher, eds.), Plenum, New York, pp. 85–104.

    Google Scholar 

  • Krishnamoorthy, M. S., and Deo, N. (1979), Node-deletion NP-complete problems,SIAM J. Comput. 8, 619–625.

    Google Scholar 

  • Lakshmipathy, N., and Winklmann, K. (1986), “Global” graph problems tend to be intractable,J. Comput. System Sci. 32, 407–428.

    Google Scholar 

  • Papadimitriou, C. H., and Sipser, M. (1984), Communication complexity,J. Comput. System Sci. 28, 260–269.

    Google Scholar 

  • Yao, A. C. (1979), Some complexity questions related to distributive computing, inProc. 11th Ann. ACM Symposium on Theory of Computing, New York, pp. 209–213.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Wartburg College, 50677-1003, Waverly, IA, USA

    William Slough

  2. Department of Computer Science, University of Colorado, 80309-0430, Boulder, CO, USA

    Karl Winklmann

Authors
  1. William Slough
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  2. Karl Winklmann
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Additional information

The work of W. Slough was supported in part by a Chevron Fellowship while he was at Washington State University. Some of the results reported in this paper were obtained while he was completing his Ph.D. thesis under the direction of K. Winklmann at Washington State University. The work of K. Winklmann was supported in part by National Science Foundation Grants MCS-80004128 DCR-8202964, DCR-8500741, and CCR-8702275 and by Grant A-0369 of the Natural Sciences and Engineering Research Council of Canada and was conducted partly at Washington State University and at the University of Alberta.

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Slough, W., Winklmann, K. On limitations of transformations between combinatorial problems. Math. Systems Theory 24, 149–168 (1991). https://doi.org/10.1007/BF02090395

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  • DOI: https://doi.org/10.1007/BF02090395

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