Lower bounds for dynamic data structures on algebraic RAMs

Algorithmica (New York)

Volumn 32, Issue 3, 2002, Pages 364-395

  Ben Amram, A M ^a   Galil, Z ^b  

^a ACADEMIC COLLEGE OF TEL AVIV YAFFO   (Israel)

^b Columbia University ^*  (United States)

Author keywords

Cell probe lower bounds; Dynamic prefix sum; Random access machine; Union find

Indexed keywords

ALGEBRA; COMPUTATIONAL METHODS; DATA STORAGE EQUIPMENT; DATA STRUCTURES; PROBLEM SOLVING;

CELL PROBE MODELS;

RANDOM ACCESS STORAGE;

EID: 0141888223     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00453-001-0079-6     Document Type: Article

References (32)

1. A. V. Aho, J. E. Hopcroft and J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA, 1974.
2. S. Alstrup, A. M. Ben-Amram and T. Rauhe, Worst-case and amortised optimality in union-find, Proc. 31st ACM Symp. on Theory of Computing (STOC), 1999, pp. 499-506.
3. A. M. Ben-Amram, On the Power of Random Access Machines, Thesis, Tel-Aviv University, 1995.
4. A.M. Ben-Amram and Z. Galil, Lower bounds for data structure problems in RAMs, Proc. 32nd Annual IEEE Symp. on Foundations of Computer Science (FOCS), San Juan, PR, 1991, pp. 622-631.
5. A. M. Ben-Amram and Z. Galil, A generalization of a lower bound technique due to Fredman and Saks, Algorithmica 30:1 (2001), 34-66.
6. A. M. Ben-Amram and Z. Galil, Topological lower bounds for algebraic random access machines, SIAM J. Comput., to appear.
7. M. Ben-Or, Lower bounds on algebraic computation trees, Proc. 15th Annual ACM Symp. on Theory of Computing (STOC), 1983, pp. 80-86.
8. N. Blum, On the single-operation worst-case time complexity of the disjoint set union problem, SIAM J. Comput. 15:4 (1986), 1021-1024.
9. N. H. Bshouty, Lower bounds for the complexity of functions in random access machines, J. Assoc. Comput. Mach. 40:2 (1993), 211-223.
10. S. A. Cook and R. A. Reckhow, Time bounded random access machines, J. Comput. System Sci. 7:4 (1973), 354-375.
11. P. F. Dietz, Optimal algorithms for list indexing and subset rank, Proc. Workshop on Algorithms and Data Structures (WADS), 1989, pp. 39-46.
12. E. Dittert and M. J. O'Donnell, Lower bounds for sorting with realistic instruction sets, IEEE Trans. Comput. C-34:4 (1985), 311-317.
13. F. E. Fich and P. B. Miltersen, Tables should be sorted (on Random Access Machines), Proc. 4th International Workshop on Algorithms and Data Structures (WADS), 1995, Lecture Notes in Computer Science 955, Springer-Verlag, Berlin, pp. 482-494.
14. G. S. Frandsen, J. P. Hansen and P. B. Miltersen, Lower bounds for dynamic algebraic problems, Proc. 16th Symp. on Theoretical Aspects of Computer Science (STAGS), 1999, Lecture Notes in Computer Science 1563, Springer-Verlag, Berlin, pp. 362-372.
15. M. L. Fredman, The complexity of maintaining an array and computing its partial sums, J. Assoc. Comput. Mach. 29:1 (1982), 250-260.
16. M. L. Fredman and M. Rauch Henzinger, Lower bounds for fully dynamic connectivity problems in graphs, Algorithmica 22:3 (1998), 351-362.
17. M. L. Fredman and M. E. Saks, On the cell probe complexity of dynamic data structures, Proc. 21st Annual ACM Symp. on Theory of Computing, Seattle, WA, 1989, pp. 345-354.
18. H. N. Gabow, Data structures for weighted matching and nearest common ancestors with linking, Proc. 1st Symp. on Discrete Algorithms (SODA), 1990, pp. 434-443.
19. Z. Galil and G. F. Italiano, Data structures and algorithms for disjoint set union problems, ACM Comput. Surveys 23:3 (1991), pp. 319-344.
20. T. Hagerup, Sorting and searching on the word RAM, Proc. 15th Symp. on Theoretical Aspects of Computer Science (STACS), 1998, Lecture Notes in Computer Science 1373, Springer-Verlag, Berlin, pp. 366-398.
21. J. Heinz and C. P. Schnorr, Testing polynomials which are easy to compute, Proc. 12th Annual ACM Symp. on Theory of Computing (STOC), Los Angeles, CA, 1980, pp. 262-272.
22. T. Husfeldt, T. Rauhe and S. Skyum, Lower bounds for dynamic transitive closure, planar point location, and parentheses matching, Nordic J. Comput. 3 (1996), 323-336.
23. K. Kendig, Elementary Algebraic Geometry, Springer-Verlag, New York, 1977.
24. P. Klein and F. Meyer auf der Heide, A lower time bound for the knapsack problem on random access machines, Acta Inform. 19 (1983), 385-395.
25. J. A. La Poutré, New techniques for the union-find problem, Proc. First Annual ACM-SIAM Symp. on Discrete Algorithms (1990), pp. 54-63. Full version: Technical Report RUU-CS-89-19, Department of Computer Science, Utrecht University, 1989.
26. F. Meyer auf der Heide, Lower bounds for solving linear diophantine equations on random access machines, J. Assoc. Comput. Mach. 32:4 (1985), 929-937.
27. W. Paul and J. Simon, Decision trees and random access machines, in Logic and Algorithmic, monographie n° 30 de l'enseignement mathématique, Université de Genève, 1982; see also K. Mehlhom, Sorting and Searching,volume 1 of Data Structures and Algorithms, Springer-Verlag, New York, 1984, pp. 85-94.
28. W. Paul and J. Simon, Decision trees and random access machines, in Logic and Algorithmic, monographie n° 30 de l'enseignement mathématique, Université de Genève, 1982; see also K. Mehlhom, Sorting and Searching,volume 1 of Data Structures and Algorithms, Springer-Verlag, New York, 1984, pp. 85-94.
29. F. P. Preparata and M. I. Shamos, Computational Geometry: An Introduction, 2nd printing, Springer-Verlag, 1985/1988.
30. M. H. M. Smid, A data structure for the Union-Find problem having good single-operation complexity, in ALCOM: Algorithms Review, Newsletter of the ESPRIT II Basic Research Actions Program Project no. 3075 (ALCOM), 1990.
31. R. E. Tarjan, Data Structures and Network Algorithms, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1983.
32. H. E. Warren, Lower bounds for approximation by nonlinear manifolds, Trans. Amer. Math. Soc. 133:1 (1968), 167-178.