Efficient time complexities for partial ordered sets or posets are well-researched field. Hopcroft and Karp introduced an algorithm that solves the minimal chain decomposition in O (n2.5) time. Felsner et al. proposed reduces complexity to (kn2) such n is number of elements poset k its width. The main goal this paper proposing efficient compute width a given partially set P according Dilworth’s...

We consider the problem of searching for a given element in a partially ordered set. More precisely, we address the problem of computing efficiently near-optimal search strategies for typical partial orders. We consider two classical models for random partial orders, the random graph model and the uniform model. We shall show that certain simple, fast algorithms are able to produce nearly-optim...

It is known that the \pattern containment" order on permutations is not a partial well-order. Nevertheless, many naturally de ned subsets of permutations are partially well-ordered, in which case they have a strong nite basis property. Several classes are proved to be partially well-ordered under pattern containment. Conversely, a number of new antichains are exhibited that give some insight as...

In this paper, we extend the domains of affirmation and negation operators, and more important, of triangular (semi)norms and (semi)conorms from the unit interval to bounded partially ordered sets. The fundamental properties of the original operators are proven to be conserved under this extension. This clearly shows that they are essentially based upon order-theoretic notions. Consequently, a ...

It is shown that under GCH every poset preserves its cofinality in any cofinality preserving extension. On the other hand, starting with ω measurable cardinals, a model with a partial ordered set which can change its cofinality in a cofinality preserving extension is constructed.

We prove that if P is a partial order and P → (ω)ω, then (a) P → (ω + ω + 1, 4)3, and (b) P → (ω +m,n)3 for each m,n < ω. Together these results represent the best progress known to us on the following question of P. Erdős and others. If P → (ω)ω, then does P → (α, n)3 for each α < ω1 and each n < ω?

A preference relation is a total order on a finite set and a quasipreference relation is a partial order. This paper first introduces the classic axiomatic property of preference relation, and develops a similar axiom for the quasi-preference relation.

The dualization problem on arbitrary posets is a crucial step in many applications in logics, databases, artificial intelligence and pattern mining. The objective of this paper is to study reductions of the dualization problem on arbitrary posets to the dualization problem on boolean lattices, for which output quasi-polynomial time algorithms exist. We introduce convex embedding and poset refle...