Abstract
The purpose of this paper is to review the origins and motivation for the conjecture that sparse NP complete sets do not exist (unless P = NP) and to describe the development of the ideas and techniques which led to the recent solution of this conjecture.
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References
Aho, A.V., Hopcroft, J.E., and Ullman, J.D., The Design and Analysis of Computer Algorithms, Addison-Wesley (1974).
Berman, P. “Relationship Between Density and Deterministic Complexity of NP-Complete Languages,” Fifth Int. Colloquium on Automata, Languages and Programming, Italy (July 1978), Springer-Verlag Lecture Notes in Computer Science Vol. 62, pp. 63–71.
Berman, L. and Hartmanis, J., “On Isomorphisms and Density of NP and Other Complete Sets,” SIAM J. Comput., 6 (1977), pp. 305–322. See also Proceedings 8th Annual ACM Symposium on Theory of Computing, (1976) pp. 30–40.
Book, R., Wrathall, C., Selman, A., and Dobkin, D., “Inclusion Complete Tally Languages and the Hartmanis-Berman Conjecture.”
Cook, S.A., “The Complexity of Theorem Proving Procedures,” Proc. 3rd Annual ACM Symposium on Theory of Computing, (1977) pp. 151–158.
Fortune, S., “A Note on Sparse Complete Sets,” SIAM J. Comput., (1979), pp. 431–433.
Garey, M.R., and Johnson, D.S., “Computers and Intractability, A Guide to the Theory of NP-Completeness,” W.H. Freeman and Co., San Francisco, 1979.
Hartmanis, J., and Berman, L., “On Polynomial Time Isomorphisms of Complete Sets,” Theoretical Computer Science, 3rd GI Conference, March, 1977, Lecture Notes in Computer Science, Vol. 48, Springer-Verlag, Heidelberg, pp. 1–15.
Hartmanis, J., and Berman, L., “On Polynomial Time Isomorphisms of Some New Complete Sets,” J. of Computer and System Sciences, Vol. 16 (1978), pp. 418–422.
Hartmanis, J., and Mahaney, S.R., “On Census Complexity and Sparseness of NP-Complete Sets,” Department of Computer Science, Cornell University, Technical Report TR 80-416 (April 1980).
Karp, R., “Reducibility Among Combinatorial Problems,” in Complexity of Computer Computations (R.E. Miller and J.W. Thatcher, eds.), Plenum, New York (1972).
Karp, R.M., and Lipton, R.J., “Some Connections between Nonuniform and Uniform Complexity Classes,” Proc. 12th ACM Symposium on Theory of Computing, (May 1980).
Ladner, R.E., “On the Structure of Polynomial Time Reducibility,” J. Assoc. Computing Machinery, Vol. 22 (1975), pp. 155–171.
Landweber, L.H., Lipton, R.J., and Robertson, E.L., “On the Structure of Sets in NP and Other Complexity Classes,” Computer Science Tech. Report 342 (December 19/8), University of Wisconsin-Madison.
Mahaney, S.R., “Sparse Complete Sets for NP: Solution of a Conjecture by Berman and Hartmanis,” Department of Computer Science, Cornell University, Technical Report TR 80-417 (April 1980).
Patterson, M, and Meyer, A.R., “With What Frequency are Apparently Intractable Problems Difficult?”, Laboratory for Computer Science, M.I.T. Tech. Report., February 1979.
Stockmeyer, L.J., “The Polynomial-Time Hierarchy,” Theoretical Computer Science Vol. 3, (1977), pp. 1–22.
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Hartmanis, J., Mahaney, S.R. (1980). An essay about research on sparse NP complete sets. In: Dembiński, P. (eds) Mathematical Foundations of Computer Science 1980. MFCS 1980. Lecture Notes in Computer Science, vol 88. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022494
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DOI: https://doi.org/10.1007/BFb0022494
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