skip to main content
article
Free Access

Applications of Path Compression on Balanced Trees

Published:01 October 1979Publication History
First page image

References

  1. 1 ACKERMANNN, W Zum Hdbershen Aufbau der reellen Zahlen. Math. Ann 99 (1928), 118-133Google ScholarGoogle Scholar
  2. 2 Aao, A.V, HOPCROFr, J.E., A~D Ut&MAN, J.D The Design and Analysts of Computer Algorithms. Addison- Wesley, Reading, Mass., 1974 Google ScholarGoogle Scholar
  3. 3 AHO, A.V, HOPCROFT, J.E, AND ULLMAN, J.D On computing least common ancestors in trees SIAM J. Comptng. 5 (1976), 115-132.Google ScholarGoogle Scholar
  4. 4 Auo, A V., AtqD UtJ~tAN, J D. Node listings for reducible flow graphs. J Comptr Syst Sci. 13 (1976), 286- 299Google ScholarGoogle Scholar
  5. 5 ARDEN, B.W., GXLLER, B A., AND GRAHAM, R.M. An algorithm for equivalence declarauons. Comm. A CM 4, 7 (July 1961), 310-314 Google ScholarGoogle Scholar
  6. 6 CHERITON, D, AND TARJAN, R E Fmdmg minimum spannmg trees SIAM J Comptng. 5 (1976), 724-742Google ScholarGoogle Scholar
  7. 7 CmN, FY, AND HOUCK, D J Algorithms for updating minimal spanning trees. J. Comptr Syst Sci 16 (1978), 333-344Google ScholarGoogle Scholar
  8. 8 CHV.~TAL, V., KLARNER, D.A., AND KNUTH, D E Selected combinatorial research problems STAN-CS-72-Google ScholarGoogle Scholar
  9. 9 FARROW, R Efficlent on-line evaluation of funcUons defined on paths m trees. Tech. Re~. 476-093-17, Dept 292, Comptr Sc~ Dept, Stanford U, Stanford, Cahf, 1972 Math Sc~, R~ce U, Houston, Tex, 1977Google ScholarGoogle Scholar
  10. 10 FISCHER, M J. Efficiency of eqmvalence algorithms. In Complexity of Computauons, R E Miller and J W Thatcher, Eds, Plenum Press, New York, 1972, pp 153-168Google ScholarGoogle Scholar
  11. 11 FONG, A., KAM, J, AND ULLMAN, J D Application of latuce algebra to loop optimization. Conf. Rec Second ACM Symp. Pnnc~ples of Programming Languages, Palo Alto, Cahf., 1975, pp 1-9 Google ScholarGoogle Scholar
  12. 12 GALLER, B A., AND FISCHER, M J An improved equivalence algorithm Comm. ACM 7, 5 (May 1964), 301- 303. Google ScholarGoogle Scholar
  13. 13 GRAHAM, S L, AND WEGMAN, M A fast and usually linear algorithm for global flow analysts. J. A CM 23, 1 (Jan 1976), 172-202 Google ScholarGoogle Scholar
  14. 14 HOPCROFT, J E Private commumcatlon.Google ScholarGoogle Scholar
  15. 15 HOPCROFT, J E., AND ULLMAN, J D Set-merging algonthms. SIAM J Comptng 2 (1973), 294-303Google ScholarGoogle Scholar
  16. 16 Hu,T C Integer Programming and Network Flows. Addison-Wesley, Reading, Mass., 1969, pp 129-150.Google ScholarGoogle Scholar
  17. 17 KENNEDY, K.W Node hstmgs applied to data flow analysis Conf Rec. Second ACM Syrup Pnnclples of Programming Languages, Palo Alto, Cahf, 1975, pp 10-21. Google ScholarGoogle Scholar
  18. 18 KNUTH, D E The Art of Computer Programming, Vol I. Fundamental Algoruhms, Addison-Wesley, Reading, Mass., 1968 Google ScholarGoogle Scholar
  19. 19 LENGAUER, T., AND TARJAN, R E A fast algonthm for finding dominators m a flow graph. To appear m A CM Tram Programming Languages and Syst. Google ScholarGoogle Scholar
  20. 20 PATERSON, M Unpubhshed report, U. of Warwick, Conventry, England, 1972.Google ScholarGoogle Scholar
  21. 21 TARJAN, R.E Depth-first search and hnear graph algorithms SlAM Z Comptng. 1 (1972), 146-160.Google ScholarGoogle Scholar
  22. 22 TAR/AN, R.E Finding dominators m directed~raphs. SlAM J. Comptng 5 (1974), 62-89.Google ScholarGoogle Scholar
  23. 23 TARJAN, R.E. Testing flow graph reduclbdlty J Comptr and Syst. Scz 9 (1974), 355-365Google ScholarGoogle Scholar
  24. 24 TAR/AN, R E Efficiency of a good but not linear set union algorithm J. ACM 22, 2 (April 1975), 215-225. Google ScholarGoogle Scholar
  25. 25 TAR/AN, R E. Apphcat~ons of path compression on balanced trees Tech Rep. STAN-CS-75-512, Comptr. Sc~ Dept, Stanford U, Stanford, Cahf., 1975 Google ScholarGoogle Scholar
  26. 26 TAR/AN, R.E Solving path problems on &rected graphs Tech Rep STAN-CS-75-528, Comptr. Set. Dept, Stanford U, Stanford, Cahf, 1975 Google ScholarGoogle Scholar
  27. 27 TAt~Ar~, R.E. Graph theory and Gaussmn elLmmaUon In Sparse Matrix Computatwns, J R. Bunch and D.J. Rose, Eds., Academic Press, New York, 1976, pp. 3-22Google ScholarGoogle Scholar
  28. 28 TAR/AN, R E A class of algorithms which reqmre non-hnear tune to maintain disjoint sets TO appear in J. Comptr and Syst. SclGoogle ScholarGoogle Scholar
  29. 29 TAR/AN, R.E ComplexRy of monotone networks for computing conjunctions Annals Discrete Math. 2 (1978), 121-133Google ScholarGoogle Scholar
  30. 30 ULLMAN, J.D. A fast algonthm for the ehmmation of common subexpresstons. Aeta Informatwa 2 (1973), 191-213.Google ScholarGoogle Scholar
  31. 31 YAO, A.C. An O({EI log log I VI) algonthm for finding minimum spanning trees. Inform. Processing Letters 4 (1975), 21-23Google ScholarGoogle Scholar

Index Terms

  1. Applications of Path Compression on Balanced Trees

      Recommendations

      Comments

      Login options

      Check if you have access through your login credentials or your institution to get full access on this article.

      Sign in

      Full Access

      • Published in

        cover image Journal of the ACM
        Journal of the ACM  Volume 26, Issue 4
        Oct. 1979
        231 pages
        ISSN:0004-5411
        EISSN:1557-735X
        DOI:10.1145/322154
        Issue’s Table of Contents

        Copyright © 1979 ACM

        Publisher

        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 1 October 1979
        Published in jacm Volume 26, Issue 4

        Permissions

        Request permissions about this article.

        Request Permissions

        Check for updates

        Qualifiers

        • article

      PDF Format

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader