Given an undirected n-node unweighted graph G = (V,E), a spanner with stretch function f(·) is a subgraph H ⊆ G such that, if two nodes are at distance d in G, then they are at distance at most f(d) in H. Spanners are very well studied in the literature. The typical goal is to construct the sparsest possible spanner for a given stretch function. In this paper we study pairwise spanners, where w...

in the transformation semigroup (x, s) we introduce the height of a closed nonempty invariant subset of x, define the transformed dimension of nonempty subset s of x and obtain some results and relations.

Recently, B. Ozbagci and A. Stipsicz [12] proved that there are infinitely many pairwise nonhomeomorphic 4-manifolds admitting genus-2 Lefschetz fibration over S but not carrying any complex structure with either orientation. (For the definition of Lefschetz fibration, see [6].) Their result depends on a relation in the mapping class group of a closed orientable surface of genus 2. This relatio...

We determine the velocity correlation function, pairwise peculiar velocity di erence, and root-mean-square pairwise peculiar velocity dispersion of rich clusters of galaxies, as a function of pair separation, for three cosmological models: = 1 and = 0:3 CDM, and = 0:3 PBI models (all at and COBEnormalized). We nd that close cluster pairs, with separation r 10h 1Mpc, exhibit strong attractive pe...

In the Maximum Weight Independent Set problem, the input is a graph G, every vertex has a non-negative integer weight, and the task is to find a set S of pairwise non-adjacent vertices, maximizing the total weight of the vertices in S. We give an nO(log 2 n) time algorithm for this problem on graphs excluding the path P6 on 6 vertices as an induced subgraph. Currently, there is no constant k kn...

In the present paper we introduce and study the notion of pairwise weakly Lindelof bitopological spaces and obtain some results. Further, we also study the pairwise weakly Lindelof subspaces and subsets, and investigate some of their properties. It was proved that a pairwise weakly Lindelof property is not a hereditary property.

Our system treats coreference resolution as an integer linear programming (ILP) problem. Extending Denis and Baldridge (2007) and Finkel andManning (2008)’s work, we exploit loose transitivity constraints on coreference pairs. Instead of enforcing transitivity closure constraints, which brings O(n3) complexity, we employ a strategy to reduce the number of constraints without large performance d...