A number of different techniques have been introduced in the last few decades to create -free automata representing regular expressions such as the Glushkov automata, follow automata, or Antimirov automata. This paper presents a simple and unified view of all these construction methods both for unweighted and weighted regular expressions. It describes simpler algorithms with time complexities a...

We give a general framework for approximate query processing in semistructured databases. We focus on regular path queries, which are the integral part of most of the query languages for semistructured databases. To enable approximations, we allow the regular path queries to be distorted. The distortions are expressed in the system by using weighted regular expressions, which correspond to weig...

In this article we consider the initial value problem of the binormal flow with initial data given by curves that are regular except at one point where they have a corner. We prove that under suitable conditions on the initial data a unique regular solution exists for strictly positive and strictly negative times. Moreover, this solution satisfies a weak version of the equation for all times an...

A set of n points in the plane is in equiangular configuration if there exist a center and an ordering of the points such that the angle of each two adjacent points w.r.t. the center is 360 ◦ n , i.e., if all angles between adjacent points are equal. We show that there is at most one center of equiangularity, and we give a linear time algorithm that decides whether a given point set is in equia...

In this paper, we study distributed algorithms to compute a weighted matching that have constant (or at least sub-logarithmic) running time and that achieve approximation ratio 2 + ǫ or better. In fact we present two such synchronous algorithms, that work on arbitrary weighted trees. The first algorithm is a randomised distributed algorithm that computes a weighted matching of an arbitrary weig...

We consider regular variation for marked point processes with independent heavy-tailed marks and prove a single large heuristic: the limit measure is concentrated on cone of measures one point. then investigate successive hidden removing at most k points, k≥1, multiple phenomenon: k+1 points. show how these results imply in Skorokhod space associated risk process, connection single/multiple heu...

This paper examines the relationship between road directions and the rectilinear distance in regular point patterns. We derive the distributions of the rectilinear distances to the nearest and the second nearest points in rotated regular point patterns. These distributions demonstrate that road directions significantly affect the rectilinear distances. As an application of the nearest and the s...

In this paper an extension will be given of a theorem of the author'sf which states that if A and B are any two points of a continuous curve M, and K denotes the set of all those points of M which separate} A and B in M, then K+A+B is a closed set of points. I t will be shown that if A and B are any two points of any connected and regular (connected im kleinen) point set M, and K denotes the se...