The Poset Cover Problem

Heath, Lenwood S.; Nema, Ajit Kumar

doi:10.4236/ojdm.2013.33020

Cited by 6 publications

(10 citation statements)

References 39 publications

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“…(1, 3), (1,4), (1,5), (2,4), (3, 5)} a. P = (V, < P ) Every poset P = (V, < P ) also corresponds to a directed acyclic graph (DAG) G = (V, A) having the vertex set V and the edge set A = {(u, v)|(u, v) ∈< P }. However, a poset is more commonly illustrated using a Hasse diagram that corresponds to the transitive reduction of the DAG.…”

Section: Introductionmentioning

confidence: 99%

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On Finding Two Posets that Cover Given Linear Orders

2019

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The Poset Cover Problem is an optimization problem where the goal is to determine a minimum set of posets that covers a given set of linear orders. This problem is relevant in the field of data mining, specifically in determining directed networks or models that explain the ordering of objects in a large sequential dataset. It is already known that the decision version of the problem is NP-Hard while its variation where the goal is to determine only a single poset that covers the input is in P. In this study, we investigate the variation, which we call the 2-Poset Cover Problem, where the goal is to determine two posets, if they exist, that cover the given linear orders. We derive properties on posets, which leads to an exact solution for the 2-Poset Cover Problem. Although the algorithm runs in exponential-time, it is still significantly faster than a brute-force solution. Moreover, we show that when the posets being considered are tree-posets, the running-time of the algorithm becomes polynomial, which proves that the more restricted variation, which we called the 2-Tree-Poset Cover Problem, is also in P.

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Section: Introductionmentioning

confidence: 99%

“…The reverse problem where the given is a set of linear extensions, or more technically a set of linear orders, and the goal is to determine the set of posets that generate the given linear orders is the Poset Cover Problem. Formally, the Poset Cover Problem is defined as follows [3]:…”

Section: Introductionmentioning

confidence: 99%

On Finding Two Posets that Cover Given Linear Orders

2019

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“…Hence, the Poset Cover problem is usually the one that must be addressed. Heath and Nema [16], however, have recently proved that Poset Cover is NP-complete. Hence, to investigate polynomial-time solvable variants of Poset Cover, we restrict our attention to poset covers whose elements come from a particular class.…”

Section: Poset Covermentioning

confidence: 99%

“…We now show the NP-completeness of COVER HAMMOCK(2,2,2) , using a reduction similar to that in Heath and Nema [16]. In particular, we reduce from Cubic Vertex Cover, a known NP-complete problem (see [13]), which is defined here.…”

Section: Poset Covermentioning

confidence: 99%

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Mining Posets From Linear Orders

Fernandez

Heath

Ramakrishnan

et al. 2013

Discrete Math. Algorithm. Appl.

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There has been much research on the combinatorial problem of generating the linear extensions of a given poset. This paper focuses on the reverse of that problem, where the input is a set of linear orders, and the goal is to construct a poset or set of posets that generates the input. Such a problem finds applications in computational neuroscience, systems biology, paleontology, and physical plant engineering. In this paper, two algorithms are presented for efficiently finding a single poset, if such a poset exists, whose linear extensions are exactly the same as the input set of linear orders. The variation of the problem where a minimum set of posets that cover the input is also explored. This variation is shown to be polynomially solvable for one class of simple posets (kite(2) posets) but NP-complete for a related class (hammock(2,2,2) posets).General Terms: Algorithms.

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