Abstract
Backtracking searches for one solution only can easily be parallelized: Each processor searches a subtree of the search tree and all processors stop when one of them has found a solution. It has raised some interest that the average speedup observable may be ≩ the number of processors, a phenomenon which is called average superlinear speedup. As this observation does not seem to be provable for principal reasons (stochastic dependencies) models from which the speedup is proved are developed. In the series of papers [MoSpVo 86], [SpMoVo 87], [Sp 88] a model to explain the speedup observable with the propositional satisfiability problem is presented. This model is based on the intuitively appealing assumption (which can be verified experimentally) that some processors search subtrees with a higher proportion of solutiòn leaves than others, i.e. the solution leaves are clustered within the search tree. A similar argument is given in [RaKu 88]. We give strong evidence that these models — at least with respect to the satisfiability problem — have serious defects and develop an improved model.
Preview
Unable to display preview. Download preview PDF.
References
B. Monien, E. Speckenmeyer, O. Vornberger, Superlinear speedup for parallel backtracking, Technical Report No 30, Dept. of Math. and Comp. Sci. University of Paderborn, 1986.
E. Speckenmeyer, B. Monien, O. Vornberger, Superlinear speedup for parallel backtracking, Proc. Supercomputing 1987, LNCS 297, 985–993.
E. Speckenmeyer, Is average superlinear speedup possible? Proc. 2nd Workshop on Comp. Sci. Logic 1988, LNCS 385, 301–312.
V.N. Rao, V. Kumar, Superlinear speedup in parallel state space search, Proc. 8th Conf. on Foundations of Software Technology and Theoretical Comp. Sci. 1988, LNCS 338, 161–174.
G.A.P. Kindervater, J.K. Lenstra, Parallel computing in Combinatorial Optimization, Annals of OR 14, 1988, 245–289.
S. Chakravarty, A. Shekhawat, Parallel and serial heuristics for the minimum set cover problem, Journal of Supercomputing 5, 1992, 331–345.
W. Ertel, Parallele Suche mit randomisiertem Wettbewerb in Inferenzsystemen. PhD Thesis, Technical University of Munich, 1992.
D.P. Helmbold, C.E. McDowall, Modeling Speedup(n) greater than n, IEEE Trans. on Par. and Distr. Systems, 1(2), 1990, 250–256.
R. Mehrotra, E.F. Geringer, Superlinear speedup through randomized algorithms, Proc. Conf. on Parallel Processing 1985, 291–300.
J. Franco, M. Paull, Probabilistic analysis of the Davis-Putnam procedure for the satisfiability problem, Discr. Appl. Math. 5, 1983, 77–87.
C.A. Brown, P.W. Purdom, An average time analysis of backtracking, SIAM Jour. on Comp. 10, 1981, 583–593.
A. Ranade, Optimal speedup for backtracking search on a butterfly network, SPAA 1991, 40–48.
D.M. Nicol, Expected performance of m-solution backtracking, SIAM Journ. on Comp. 17(1), 1988, 114–127.
V. Chvatal, B. Reed, Mick gets some (the odds are on his side), Proc. FOCS 1992.
A. Goerdt, A threshold for unsatisfiability, Proc. MFCS 1992, LNCS 629, 264–275.
R. Matuschka, R. Niedermeier, Verschiedene Heuristiken für die parallele Behandlung des Erfüllbarkeitsproblems auf dem IPSC, Report of a Fortgeschrittenenpraktikum for Computer Scientists at the Technical University Munich, 1990.
R.L. Graham, D.E. Knuth, O. Patashnik, ”Concrete Mathematics”, Addison Wesley, Reading, Massachusetts, 1989.
H.A. David, Order statistics, Wiley and Sons Inc., New York, 1981.
Greene, D.E. Knuth, Mathematics for the analysis of algorithms, Birkhäuser.
M. Kendall, A. Stuart, J.K. Ord, Kendall's advanced theory of statistics, vol. 1, Griffin, London, 1987.
D.S. Mitrinovic, Analytic inequalities, Springer, Berlin, 1970.
H.O. Hartley, H.A. David, Universal bounds for mean range and extreme observation, Ann. Math. Statist 25, 1954, 84–99.
I. Althöfer, Communication of I. Althöfer about a talk of de la Vega.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Goerdt, A., Kamps, U. (1994). On the reasons for average superlinear speedup in parallel backtrack search. In: Börger, E., Gurevich, Y., Meinke, K. (eds) Computer Science Logic. CSL 1993. Lecture Notes in Computer Science, vol 832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0049327
Download citation
DOI: https://doi.org/10.1007/BFb0049327
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58277-9
Online ISBN: 978-3-540-48599-5
eBook Packages: Springer Book Archive