Embedding Ordered Sets into Distributive Lattices

被引：5

作者：

Van Alten, C. J. ^{[1
]}

机构：

[1] Univ Witwatersrand, Sch Comp Sci & Appl Math, Private Bag 3, ZA-2050 Johannesburg, South Africa

来源：

ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS | 2016年 / 33卷 / 03期

关键词：

Ordered set; Distributive lattice; NP-complete; DIMENSION; POSETS;

D O I：

10.1007/s11083-015-9376-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：419 / 427

页数：9

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