Algorithms over partially ordered sets
- 45 Downloads
We here study some problems concerned with the computational analysis of finite partially ordered sets. We begin (in § 1) by showing that the matrix representation of a binary relationR may always be taken in triangular form ifR is a partial ordering. We consider (in § 2) the chain structure in partially ordered sets, answer the combinatorial question of how many maximal chains might exist in a partially ordered set withn elements, and we give an algorithm for enumerating all maximal chains. We give (in § 3) algorithms which decide whether a partially ordered set is a (lower or upper) semi-lattice, and whether a lattice has distributive, modular, and Boolean properties. Finally (in § 4) we give Algol realizations of the various algorithms.
KeywordsComputational Mathematic Matrix Representation Computational Analysis Chain Structure Maximal Chain
Unable to display preview. Download preview PDF.
- 1.G. Birkhoff,Lattice Theory, Amer. Math. Soc. Colloq. Publ. XXV, rev. ed. 1961.Google Scholar
- 2.E. Szpilrajn,Sur l'extension de l'ordre partiel, Fund. Math. 16 (1930), 386–389.Google Scholar
- 4.A Proposal for Input-Output conventions in ALGOL 60, Comm. ACM, 7 (1964), 273–283.Google Scholar
- 5.Control Data Corp., 3000/6000 Algol Generic Reference Manual, Dec. 1967, Pub. No. 60214900.Google Scholar