Opportunistic algorithms for eliminating supersets
The main problem tackled in this paper is that of finding each set in a given collection that has no proper subset in the collection. Starting with a solution that uses a quadratic (in the size of the collection) number of subset tests, solutions are developed that are opportunistic in the sense of running significantly faster for certain classes of input (such as when most sets are small), but without running slower on other input. They are based on an opportunistic algorithm for the fundamental problem of finding an element common to two ordered sequences. Methodological issues are emphasized throughout.
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- 1.Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The design and analysis of computer algorithms. Reading, MA: Addison-Wesley 1974Google Scholar
- 2.Dijkstra, E.W.: Smoothsort, an alternative for sorting in situ. Sci. Comput. Program.1, 223–233 (1982)Google Scholar
- 3.Dijkstra, E.W.: The saddleback search. Epistle EWD 934, Department of Computer Sciences, The University of Texas at Austin, September 1985Google Scholar
- 4.Dijkstra, E.W.: Fillers at the YoP Institute, in: The formal development of programs and proofs, E. W. Dijkstra (ed.), pp. 209–227. Reading,, MA: Addison-Wesley 1989Google Scholar
- 5.Dijkstra, E.W.: To hell with “meaningful identifiers” ! Epistle EWD 1044, Department of Computer Sciences, The University of Texas at Austin, February 1989Google Scholar
- 6.Dijkstra, E.W., Feijen, W.: The linear search revisited. Struct. Program.10, 5–9 (1989)Google Scholar
- 7.Dromey, R.G.: Forced termination of loops. Software: Pract. Exper.15, 30–40 (1985)Google Scholar
- 8.Gries, D.: The science of programming, Berlin Heidelberg New York: Springer 1981Google Scholar
- 9.Kirkpatrick, D, Seidel, R.: The ultimate planar convex hull algorithm? Technical Report 83-577. Department of Computer Science, Cornell University, 1983Google Scholar
- 10.Pritchard, P.: Algorithms for finding matrix models of propositional calculi. J. Autom. Reasoning (to appear)Google Scholar
- 11.Pritchard, P.: Another look at the “longest ascending subsequence” problem. Acta Inf.16, 87–91 (1981)Google Scholar
- 12.Pritchard, P.: Linear prime-number sieves: A family tree. Sci. Comput. Program.9, 17–35 (1987)Google Scholar
- 13.Pritchard, P.: An introduction to programming using Macintosh Pascal Reading, MA: Addison-Wesley 1988Google Scholar