This paper discusses activity graphs, the mathematical formalism underlying the Activity Coordination System, a process-centered system for collaborative work. The activity graph model was developed for the purpose of describing, tracking, and guiding distributed, communication-intensive activities. Its graph-based semantics encompasses the more familiar Petri nets, but has several novel proper...

We discuss general techniques, centered around the “Layerwise Separation Property” (LSP) of a planar graph problem, that allow to develop algorithms with running time c √ k|G|, given an instance G of a problem on planar graphs with parameter k. Problems having LSP include planar vertex cover, planar independent set, and planar dominating set. Extensions of our speed-up technique to basically al...

Choose random pointsX1, X2, X3, . . . independently from a uniform distribution in a unit ball in <. Call Xn a dominator iff distance(Xn, Xi) ≤ 1 for all i < n, i.e. the first n points are all contained in the unit ball that is centered at the n’th point Xn. We prove that, with probability one, only finitely many of the points are dominators. For the special casem = 2, we consider the unit disk...

We study in graphs a property related to fault-tolerance in case a node fails. A graph G is k-self-repairing, where k is a non-negative integer, if after the removal of any vertex no distance in the surviving graph increase by more than k. We give upper and lower bounds on the minimum number of edges of a k-self-repairing graph for prescribed k and n, where n is the order of the graph. We also ...

Let V be a set of distinct points in the Euclidean plane. For each point x 2 V , let sx be the ball centered at x with radius equal to the distance from x to its nearest neighbour. We refer to these balls as the spheres of in uence of the set V . The sphere of in uence graph on V is de ned as the graph where (x; y) is an edge if and only if sx and sy intersect. In this extended abstract, we dem...

Given a planar graph G, the graph theoretic dilation of G is defined as the maximum ratio of the shortestpath distance and the Euclidean distance between any two vertices of G. Given a planar point set S, a triangulation of S that achieves minimum graph theoretic dilation is called a minimum dilation triangulation of S. In this paper, we show that a simple exclusion region for an edge e of the ...

A graph is clique-Helly if any family of mutually intersecting (maximal) cliques has non-empty intersection, and it is hereditary clique-Helly (abbreviated HCH) if its induced subgraphs are clique-Helly. The clique graph of a graph G is the intersection graph of its cliques, and G is self-clique if it is connected and isomorphic to its clique graph. We show that every HCH graph is an induced su...

We have studied the development of head-centered visual responses in an unsupervised self-organizing neural network model which was trained under ecological training conditions. Four independent spatio-temporal characteristics of the training stimuli were explored to investigate the feasibility of the self-organization under more ecological conditions. First, the number of head-centered visual ...

Background: Asthma is considered as the most common chronic disease of childhood that can cause missing school and daily limits. It can also have effects on physical, psychological, and social well-being in children. Therefore, improving two indicators of self-efficacy and self-esteem seem of utmost importance in this domain. Objectives: The purpose of this study was to determine the effect of...