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On the Average Case Complexity of Some P-complete Problems

Published online by Cambridge University Press:  15 August 2002

Maria Serna  and
Fatos Xhafa
Maria Serna
Affiliation:
Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Campus Nord – C6, Jordi Girona Salgado 1-3, 08034 Barcelona, Spain; [email protected].
Fatos Xhafa
Affiliation:
Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Campus Nord – C6, Jordi Girona Salgado 1-3, 08034 Barcelona, Spain; [email protected].
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Abstract

We show that some classical P-complete problems can be solved efficiently in average NC. The probabilistic model we consider is the sample space of input descriptions of the problem with the underlying distribution being the uniform one. We present parallel algorithms that use a polynomial number of processors and have expected time upper bounded by (e ln 4 + o(1))log n, asymptotically with high probability, where n is the instance size.

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 33 , Issue 1 , January 1999 , pp. 33 - 45
Copyright
© EDP Sciences, 1999

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References

J.L. Balcázar, J. Díaz and J. Gabarró, Structural complexity II, Springer Verlag (1995).
Calkin, N. and Frieze, A., Probabilistic analysis of a parallel algorithm for finding a maximal independent set. Random Structures and Algorithms 1 (1990) 39-50. CrossRef
Cook, S.A., Observation, An on time-storage trade-offs. J. Comp. Syst. Sci. 9 (1974) 308-316. CrossRef
D. Coppersmith, P. Raghavan and M. Tompa, Parallel graph algorithms that are efficient in average, in Proc. of 28th IEEE Symposium on Foundations of Computer Science (1987) 260-269.
J. Díaz, M. Serna, P. Spirakis and J. Torán, On the expected depth of Boolean circuits. Technical Report LSI-94-7-R, Universitat Politècnica de Catalunya, Dept. de LSI (1994).
R. Greenlaw, H.J. Hoover and W.L. Ruzzo, Limits to parallel computation: P-completeness theory. Oxford University Press (1995).
J. Hoover and W. Ruzzo, A compendium of problems complete for P. Manuscript (1984).
Jones, N.D. and Laaser, T., Complete problems for deterministic polynomial time. Theoret. Comput. Sci. 3 (1977) 105-117. CrossRef
D.E. Knuth, The art of computer programming, Vol. 1. Addison-Wesley (1973).
D. Kozen, Complexity of finitely presented algebras; in Proc. of 9th ACM STOC (1977) 164-167.
Ladner, R.E., The circuit value problem is logspace complete for P. SIGACT News 7 (1975) 18-20. CrossRef
M. Serna, The parallel approximbility of P-complete problems. PhD thesis, Universitat Politècnica de Catalunya (1990).
Serna, M., Approximating linear programming is logspace complete for P. Inform. Proc. Lett. 37 (1991) 233-236. CrossRef
Sahni, S. and Gonzalez, T., P-complete approximation problems. J. Assoc. Comput. Mach. 23 (1976) 555-565. CrossRef
Serna, M. and Spirakis, P.G., The approximability of problems complete for P, in International Symposium on Optimal Algorithms, Springer-Verlag, Lecture Notes in Computer Science 401 (1989) 193-204. CrossRef
Tsukiji, T. and Xhafa, F., On the expected depth of randomly generated circuits, J. Díaz and M. Serna Eds., in Proc. of Fourth European Symposium on Algorithms, ESA'96, Springer-Verlag, Lecture Notes in Computer Science 1136 (1996) 208-220. CrossRef