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Embedding Ordered Sets into Distributive Lattices

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Abstract

This paper investigates the class of ordered sets that are embeddable into a distributive lattice in such a way that all existing finite meets and joins are preserved. The main result is that the following decision problem is NP-complete: Given a finite ordered set, is it embeddable into a distributive lattice with preservation of existing meets and joins? The NP-hardness of the problem is proved by polynomial reduction of the classical 3SAT decision problem into it, and the NP-completeness by presenting a suitable NP-algorithm.

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Authors and Affiliations

  1. School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits, 2050, South Africa

    C. J. Van Alten

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  1. C. J. Van Alten
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Correspondence to C. J. Van Alten.

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Van Alten, C.J. Embedding Ordered Sets into Distributive Lattices. Order 33, 419–427 (2016). https://doi.org/10.1007/s11083-015-9376-6

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  • DOI: https://doi.org/10.1007/s11083-015-9376-6

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