Efficient sublinear time parallel algorithms for dynamic programming and context-free recognition

  • Lawrence L. Larmore
  • Wojciech Rytter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 577)

Abstract

We design a sublinear time parallel algorithm for the computation of the general dynamic programming recurrences. Its total work matches the work of the best known sequential algorithm. It is the first optimal sublinear parallel time algorithm for this problem. Using similar methods we construct also sublinear time parallel algorithms for the recognition of linear, unambiguous and deterministic cfl's. Their total works are O(T(n)αlog(n)), for arbitrarily small constant α<1, where T(n) is the work of the best known sequential algorithm for the problem. This reduces substantially the gap between the total work of sublinear time parallel algorithms and that of the best known sequential algorithms.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AKLMT 89]
    M.Atallah, R.Kosaraju, L.Larmore, G.Miller, Teng, Parallel tree construction, SPAA'89Google Scholar
  2. [BKR 91]
    L.Banachowski, A.Kreczmar, W.Rytter, Analysis of algorithms and data structures, Chapters 6–7, Addison Wesley (1991)Google Scholar
  3. [CM 90]
    M.Chytil, B.Monien, Caterpillars and context free languages, STACS'90Google Scholar
  4. [CCMR 90]
    M.Chytil, M.Crochemore, B.Monien, W.Rytter, On the parallel recognition of unambiguous context free languages, accepted to Theoretical Computer ScienceGoogle Scholar
  5. [GR 88]
    A.Gibbons, W.Rytter, Efficient parallel algorithms, Cambridge University Press (1988)Google Scholar
  6. [GR 89]
    A.Gibbons, W.Rytter, Optimal parallel algorithm for dynamic expression evaluation and context free recognition, Information and Computation (1989)Google Scholar
  7. [GT 79]
    L.Guibas, H.Thompson, C.Thompson, Direct VLSI implementation of combinatorial algorithms, Caltech Conf. on VLSI (1979)Google Scholar
  8. [HU 79]
    J.Hopcroft, J.Ullman, Introduction to automata, languages and computation, Addison Wesley (1979)Google Scholar
  9. [HLV 90]
    S.Huang, H.Liu, V.Viswanathan, A sublinear parallel algorithm for some dynamic programming problems, Int.Conf. on Parallel Processing 3 (1990) 261–264Google Scholar
  10. [Ko 75]
    S.R.Kosaraju. Speed of recognition of context-free language by array automata, SIAM J.Comp. 4 (1975) 333–340Google Scholar
  11. [KR 88]
    P.Klein, J.Reif, Parallel time O(log n) acceptance of deterministic cfl's, SIAM Journal on Comp. 17 (19880, page 484Google Scholar
  12. [Ry 87]
    W.Rytter, Parallel time O(log n) recognition of unambiguous cfl's, Information and Computation 73 (1987) 315–322Google Scholar
  13. [Ry 88]
    W.Rytter, On the parallel computation of costs of paths on a grid graph, IPL 29 (1988) 71–74Google Scholar
  14. [Ry 85]
    W.Rytter, The complexity of two way pushdown automata and recursive programs, Combinatorial algorithms on texts (ed.A.Apostolico, R.Capocelli), Springer-Verlag (1985) 341–356Google Scholar
  15. [Ry 82]
    W.Rytter, Time complexity of unambiguous path systems, IPL 15:3 (1982)Google Scholar
  16. [VHL 90]
    V.Viswanathan, S.Huang, H.Liu, Parallel dynamic programming, IEEE Conf. on Parallel Processing (1990) 497–500Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Lawrence L. Larmore
    • 1
  • Wojciech Rytter
    • 2
  1. 1.Dept. of Computer ScienceUniversity of California at RiversideRiversideUSA
  2. 2.Institute of InformaticsWarsaw UniversityWarszawa 59Poland

Personalised recommendations