Quorum systems are a mechanism for obtaining fault-tolerance and efficient distributed systems. We consider geographic quorum systems; a geographic quorum system is a partitioning of a set X of points in the plane (representing servers) into quorums (i.e. clusters) of size k. The distance between a point p and a cluster C is the Euclidean distance between p and the farthest point in C. We prese...

Metric based comparison operations such as finding maximum, nearest and farthest neighbor are fundamental to studying various clustering techniques k -center agglomerative hierarchical clustering. These crucially rely on accurate estimation of pairwise distance between records. However, computing exact features the records, their distances is often challenging, sometimes not possible. We circum...

Pareto-optimal objects are favored as each of such objects has at least one competitive edge against all other objects, or “not dominated.” Recently, in the database literature, skyline queries have gained attention as an effective way to identify such pareto-optimal objects. In particular, this paper studies the pareto-optimal objects in perspective of facility or business locations. More spec...

Let X be an arrangement of n algebraic sets Xi in d-space, where the Xi are either parametrized or zero-sets of dimension 0 ≤ mi ≤ d − 1. We study a number of decompositions of d-space into connected regions in which the distance-squared function to X has certain invariances. Each region is contained in a single connected component of the complement of the bifurcation set B of the family of dis...

The conventional clustering algorithms mine static databases and generate a set of patterns in the form of clusters. Many real life databases keep growing incrementally. For such dynamic databases, the patterns extracted from the original database become obsolete. Thus the conventional clustering algorithms are not suitable for incremental databases due to lack of capability to modify the clust...

In this note, we outline a very simple algorithm for the following problem: Given a set S of n points p1, p2, p3, . . . , pn in the plane, we have O(n ) segments implicitly defined on pairs of these n points. For each point pi, find a segment from this set of implicitly defined segments that is farthest from pi. The complexity of our algorithm is in O(nh+n logn), where n is the number of input ...

The demonstration of repeated gamma-ray bursts from an individual source would severely constrain burst source models. Recent reports (Quashnock & Lamb 1993; Wang & Lingenfelter 1993) of evidence for repetition in the rst BATSE burst catalog have generated renewed interest in this issue. Here, we analyze the angular distribution of 585 bursts of the second BATSE catalog (Meegan et al. 1994). We...

This article considers a family of functionals J to be maximized over the planar convex sets K for which the perimeter and Steiner point have been fixed. Assuming that J is the integral of a quadratic expression in the support function h, the maximizer is always either a triangle or a line segment (which can be considered as a collapsed triangle). Among the concrete consequences of the main the...

We study the reverse triangle inequalities for suprema of logarithmic potentials on compact sets of the plane. This research is motivated by the inequalities for products of supremum norms of polynomials. We find sharp additive constants in the inequalities for potentials, and give applications of our results to the generalized polynomials. We also obtain sharp inequalities for products of norm...