Lowest common ancestors in trees and directed acyclic graphs

Journal of Algorithms

Volumn 57, Issue 2, 2005, Pages 75-94

  Bender, Michael A ^a   Farach Colton, Martín ^b   Pemmasani, Giridhar ^a   Skiena, Steven ^a   Sumazin, Pavel ^c  

^a Stony Brook University   (United States)

^b RUTGERS UNIVERSITY   (United States)

^c Department of Electrical and Computer Engineering   (United States)

Author keywords

Cartesian tree; Directed cyclic graph (DAG); Lowest common ancestor (LCA); Range minimum query (RMQ); Shortest path

Indexed keywords

ALGORITHMS; MATHEMATICAL MODELS; PROBLEM SOLVING;

CARTASIAN TREE; DIRECTED CYCLIC GRAPH (DAG); LOWEST COMMON ANCESTOR (LCA); RANGE MINIMUM QUERY (RMQ); SHORTEST PATH;

TREES (MATHEMATICS);

EID: 27144489067     PISSN: 01966774     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jalgor.2005.08.001     Document Type: Article

References (29)

1. H. Ait-Kaci, R. Boyer, P. Lincoln, and R. Nasr Efficient implementation of lattice operations ACM Trans. Program. Lang. Syst. 11 1 1989 115 146
2. M.A. Bender, and M. Farach-Colton The LCA problem revisited Latin American Theoretical Informatics 2000 88 94
3. M.A. Bender, G. Pemmasani, S. Skiena, and P. Sumazin Finding least common ancestors in directed acyclic graphs Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms 2001 ACM Press 235 244
4. O. Berkman, and U. Vishkin Recursive star-tree parallel data structure SIAM J. Comput. 22 2 1993 221 242
5. O. Berkman, and U. Vishkin Finding level-ancestors in trees J. Comput. System Sci. 48 2 1994 214 230
6. J. Bilmes, K. Asanović, C. Whye Chin, and J. Demmel Optimizing matrix multiply using PHiPAC: a portable, high-performance, ANSI C coding methodology Proceedings of International Conference on Supercomputing Vienna, Austria, July 1997 1977 ACM Press
7. J. Bilmes, K. Asanović, C. whye Chin, and J. Demmel Using PHiPAC to speed error back-propagation learning Munich, Germany, April 1997 Proceedings of ICASSP vol. 5 1997 IEEE Press 4153 4157
8. V. Bouchitté, and J.-X. Rampon On-line algorithms for orders Theoret. Comput. Sci. 175 2 1997 225 238
9. R. Cole, and R. Hariharan Dynamic LCA queries on trees Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms 1999 ACM Press 235 244
10. D. Coppersmith, and S. Winograd Matrix multiplication via arithmetic progressions Proceedings of the Nineteenth Annual ACM Symposium on Theory of Computing New York City, 25-27 May 1987 1987 ACM Press 1 6
11. R. Ducournau, and M. Habib On some algorithms for multiple inheritance in object-oriented programming J. Bézivin J.-M. Hullot P. Cointe H. Lieberman ECOOP'87 European Conference on Object-Oriented Programming Paris, France, 15-17 June 1987 Lecture Notes in Comput. Sci. vol. 276 1987 Springer 243 252
12. A. Fall, Reasoning with Taxonomies, PhD thesis, Simon Fraser University, Burnaby, British Columbia, Canada, 1990
13. A. Fall, An abstract framework for taxonomic encoding, in: Proceedings First International Symposium on Knowledge Retrieval, Use and Storage for Efficiency, 1995
14. H.N. Gabow, J.L. Bentley, and R.E. Tarjan Scaling and related techniques for geometry problems Proceedings of the 16th Annual ACM Symposium on Theory of Computing 1984 ACM Press 135 143
15. H.N. Gabow, and R.E. Tarjan A linear-time algorithm for a special case of disjoint set union Proceedings of the 15th Annual ACM Symposium on Theory of Computing 1983 ACM Press 246 251
16. A. Goldberg, and D. Robson SmallTalk-80: The Language and Its Implementation 1980 Addison-Wesley Reading, MA
17. M. Habib, M. Huchard, and J. Spinrad A linear algorithm to decompose inheritance graphs into modules Algorithmica 13 6 1995 573 591
18. M. Habib, and L. Nourine Structure for distributive lattices and applications Theoret. Comput. Sci. 165 2 1996 391 405
19. D. Harel, and R.E. Tarjan Fast algorithms for finding nearest common ancestors SIAM J. Comput. 13 2 1984 338 355
20. G.-V. Jourdan, J.-X. Rampon, and C. Jard Computing on-line the lattice of maximal antichains of posets Order 11 2 1994 197 210
21. D. McAllester Boolean class expressions ACM SIGPLAN Notices 21 11 1986 417 423
22. M. Morvan, L. Nourine, Generating minimal interval extentions, Research Report No. 92-015, LIRMM, Montpellier, 1992
23. M. Nykänen, and E. Ukkonen Finding lowest common ancestors in arbitrarily directed trees Inform. Process. Lett. 50 6 1994 307 310
24. D.S. Parker Partial order programming Sixteenth Annual ACM Symposium on Principles of Programming Languages Austin, Texas 1989 ACM Press 260 266
25. B. Schieber, and U. Vishkin On finding lowest common ancestors: Simplification and parallelization SIAM J. Comput. 17 1988 1253 1262
26. R.E. Tarjan Applications of path compression on balanced trees J. ACM 26 4 1979 690 715
27. B. Wang, J. Tsai, and Y. Chuang The lowest common ancestor problem on a tree with unfixed root Inform. Sci. 119 1999 125 130
28. Z. Wen New algorithms for the LCA problem and the binary tree reconstruction problem Inform. Process. Lett. 51 1 1994 11 16
29. U. Zwick All pairs shortest paths in weighted directed graphs - exact and almost exact algorithms Annual Symposium on Foundations of Computer Science Palo Alto, CA, USA 1998 IEEE Press 310 319