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A poset dimension algorithm.

Yañez Gestoso, Francisco Javier and Montero de Juan, Francisco Javier (1999) A poset dimension algorithm. Journal of Algorithmst, 30 (1). pp. 185-208. ISSN 0196-6774

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Abstract

This article presents an algorithm which computes the dimension of an arbitrary finite poset (partial order set). This algorithm is based on the chromatic number of a graph instead of the classical approach based on the chromatic number of some hypergraph. The relation between both approaches is analyzed. With this algorithm, the dimension of many modest size posets can be computed. Otherwise, an upper bound for the poset dimension is obtained. Some computational results are included. (C) 1999 Academic Press.


Item Type:Article
Uncontrolled Keywords:Hypergraph; Search problem
Subjects:Sciences > Computer science > Artificial intelligence
ID Code:16800
References:

K. Bogart and W. T. Trotter, Maximal dimensional partially ordered sets III: A character-ization of Hiraguchi’s inequality for interval dimensions, Discrete Math. 15_1976.,389]400.

B. Dushnik and E. W. Miller, Partially ordered sets, Amer. J. Math. 63 _1941., 600]610.

P. C. Fishburn, ‘‘Interval Orders and Interval Graphs,’’ Wiley, New York, 1985.

P. C. Fishburn and W. T. Trotter, Posets with large dimension and relatively few critical pairs, Order 10_1993., 317]328.

M. R. Garey and D. S. Johnson, ‘‘Computer and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1978.

M. C. Golumbic, ‘‘Algorithmic Graph Theory and Perfect Graphs,’’ Academic Press, New York, 1980.

D. Kelly, The 3-irreducible partially ordered sets, Canad. J. Math. 29 _1977., 67]383.

D. Kelly and W. T. Trotter, Dimension theory for ordered sets, in ‘‘Ordered Sets’’_I. Rival, Ed.., pp. 171]212, North-Holland, Amsterdam, 1982.

H. A. Kierstead and W. T. Trotter, A note on removable pairs, in ‘‘Graph Theory,Combinatorics and Applications,’’ Vol. 2 _Y. Alavl et al., Eds.., Wiley, New York, 1991.

S. M. Korman, The graph colouring problem,in ‘‘Combinatorial Optimization’’ _N.Christophides et al., Eds.., Wiley, Chichester, 1979.

S. B. Maurer and I. Rabinovitch, Large minimal realizers of a partial order, Proc. Amer. Math. Soc. 66 _1978., 211]216.

O. Ore, ‘‘Theory of graphs,’’ Colloquium Publication, Vol. 38, American Mathematical Society, Providence, RI, 1962.

K. Reuter, Removing critical pairs, Order 6 _1989., 107]118.

W. T. Trotter, ‘‘Combinatorics and Partially Ordered Sets. Dimension Theory,’’ Johns Hopkins University Press,Baltimore, 1992.

W. T. Trotter and J. I. Moore, Characterization problems for graphs, partially ordered sets, lattices and families of sets, Discrete Math. 16 _1976., 361]381.

W. T. Trotter, J. I. Moore, and D. P. Sumner, The dimension of a comparability graph, Proc. Amer. Math. Soc. 60 _1976., 35]38.

D. B. West, Parameters of partial orders and graphs: Packing, covering, and representa-tion, in ‘‘Graphs and Orders,’’ _I. Rival, Ed.., pp. 267]350, North-Holland, Amsterdam,1985.

M. Yannakakis, On the complexity of the partial order dimension problem, SIAM J.Algebra Discrete Methods 3 _1982., 351]358.

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