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.
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页码：419 / 427
页数：9
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