Given a set S = {s1, s2, . . . , sn} of strings each of length m, and an integer L, we study the following two problems. k-Closest Substring problem: find k center strings c1, c2, . . . , ck of length L minimizing d such that for each sj ∈ S, there is a length-L substring tj (closest substring) of sj with min1≤i≤k d(ci, tj) ≤ d. We give a PTAS for this problem, for k = O(1). k-Consensus Pattern...

The spatial arrangement of a chemical compound plays an important role regarding the related properties or activities. A straightforward approach to encode the geometry is to enumerate pairwise spatial relationships between k substructures, like functional groups or subgraphs. This leads to a combinatorial explosion with the number of features of interest and redundant information. The goal of ...

We study the problem of “staying in the middle”: we have a set of points moving in a geometric space and wish to maintain another point (possibly one of the given points, but not necessarily) that stays continuously “in the middle” of the moving set. More precisely, in R we wish to maintain the median or, more generally, a point of rank k. In R we wish to maintain suitable analogs of the median...

Let K be a (commutative) locally compact hypergroup with a left Haar measure. Let L1(K) be the hypergroup algebra of K and UCl(K) be the Banach space of bounded left uniformly continuous complex-valued functions on K. In this paper we show, among other things, that the topological (algebraic) center of the Banach algebra UCl(K)* is M(K), the measure algebra of K.

Recognizing genes with distinctive expression levels can help in prevention, diagnosis and treatment of the diseases at the genomic level. In this paper, fast Global k-means (fast GKM) is developed for clustering the gene expression datasets. Fast GKM is a significant improvement of the k-means clustering method. It is an incremental clustering method which starts with one cluster. Iteratively ...

We present the first constant-factor approximation algorithm for the metric k-median problem. The k-median problem is one of the most well-studied clustering problems, i.e., those problems in which the aim is to partition a given set of points into clusters so that the points within a cluster are relatively close with respect to some measure. For the metric k-median problem, we are given n poin...

We study the 1-center problem with outliers in highdimensional data streams. The problem definition is as follows: given a sequence of n points in d dimensions (with d arbitrarily large), enclose all but z points using a ball of minimum radius.