A class of tree-like UNION-FIND data structures and the nonlinearity
This paper defines a class of tree-like data structures for the UNION-FIND problem. A structure from this class is injectable in another if each tree in the latter one can be obtained as a result of some program in the former as well. By means of injection of structures the nonlinearity in this class is proved.
Key wordscomputational complexity data structures set union trees UNION-FIND
Unable to display preview. Download preview PDF.
- A.V. Aho, J.E. Hopcroft, J.D. Ullman, "The design and analysis of computer algorithms", Addison-Wesley, Reading, MA, 2-nd printing, 1975, 124–139Google Scholar
- B.W. Arden, B.A. Galler, R.M. Graham, An algorithm for equivalence declarations, Comm. ACM 4 (7) (1961) 310–344Google Scholar
- J.E. Hopcroft, J.D. Ullman, Set merging algorithms, SIAM J. Comput. 2 (1973) 294–303Google Scholar
- A. Kirschenbaum, R. van Slyke, Computing minimum spanning trees efficiently, Proc. 25th Annual Conf. of the ACM (1972) 518–527Google Scholar
- D.E. Knuth, A. Schönhage, The expected linearity of a simple equivalence algorithm, Theoret. Comput. Sci. 6 (3) (1978) 281–315Google Scholar
- M.J. Lao, A new data structure for the UNION-FIND problem, Inform. Processing Lett. 9 (1979) 39–45Google Scholar
- R.E. Tarjan, Efficiency of a good but not linear set union algorithm, J. ACM 22 (2) (1975) 215–225Google Scholar
- R.E. Tarjan, A class of algorithms which require nonlinear time to maintain disjoint sets, J. Comp. System Sci. 2 (1979) 110–127Google Scholar