Suppose we are given a partially ordered set, a real-valued weight associated with each element and a positive integer k. We consider the problem which asks to find an ideal of size k of the partially ordered set such that the range of the weights is minimum. We call this problem the minimum-range ideal problem. This paper shows a new and fast 0 ( n log n + m) algorithm for this problem, where ...

A common fixed point result for weakly increasing mappings satisfying generalized contractive type of Zhang in ordered metric spaces are derived.

Usually, in the Kripke semantics for intuitionistic propositional logic (or for superintuitionistic logics) partially ordered frames are used. Why? In this paper we propose an intrinsically intuitionistic motivation for that. Namely, we show that every Kripke frame (with an arbitrary accessibility relation), whose set of valid formulas is a superintuitionistic logic, is logically equivalent to ...

A cocoloring of a graph G is a partition of the vertex set of G such that each set of the partition is either a clique or an independent set in G. Some special cases of the minimum cocoloring problem are of particular interest. We provide polynomial-time algorithms to approximate a minimum cocoloring on graphs, partially ordered sets and sequences. In particular, we obtain an efficient algorith...

In this paper, some categorical properties of the category ${bf Cpo}_{{bf Act}text{-}S}$ of all {cpo $S$-acts}, cpo's equipped with actions of a monoid $S$ on them, and strict continuous action-preserving maps between them is considered. In particular, we describe products and coproducts in this category, and consider monomorphisms and epimorphisms. Also, we show that the forgetful functor from...

We consider the follow poset merging problem: Let X and Y be two subsets of a partially ordered set S. Given complete information about the ordering within both X and Y , how many comparisons are needed to determine the order on X ∪ Y ? This problem is a natural generalization of the list merging problem. While searching in partially ordered sets and sorting partially ordered sets have been con...

Reported here is the discovery of a simple functional the optimization of which by a dynamical process results in extraordinary structural organization in partially ordered sets. Since partially ordered sets are one of the most prevalent and fundamental objects in Mathematics, and are ubiquitous in nature, physics, engineering and technology in general, and since any system amenable to mathemat...

A topology on a lattice L or more generally on a partially ordered set P is called an intrinsic topology if it is de ned directly from the order Early ex amples of such topologies were the interval topology of O Frink Fr and the order topology introduced by G Birkho Bi The early intrinsic topolo gies were typically symmetric i e the topology de ned on L agreed with the topology de ned on L the ...