The k-means algorithm is one of the most widely used clustering algorithms and has been applied in many fields of science and technology. One of the major problems of the k-means algorithm is that it may produce empty clusters depending on initial center vectors. For static execution of the k-means, this problem is considered insignificant and can be solved by executing the algorithm for a numb...

In this paper, we present a novel approach for discovering kinetically metastable states of biomolecular conformations. Several kinetically-aware metrics which encode both geometric and kinetic information about biomolecules are proposed. We embed the new metrics into k-center clustering and r-cover clustering algorithms to estimate the metastable states. Those clustering algorithms using kinet...

We present efficient MapReduce and Streaming algorithms for the $k$-center problem with and without outliers. Our algorithms exhibit an approximation factor which is arbitrarily close to the best possible, given enough resources.

We consider the reachability indexing problem for privatepublic directed graphs. In these graphs nodes come in three flavors: public—nodes visible to all users, private—nodes visible to a specific set of users, and protected—nodes visible to any user who can see at least one of the node’s parents. We are interested in computing the set of nodes visible to a specific user online. There are two o...

in the new production systems, finding a way to improving the product and system reliability in design is a very important. the reliability of the products and systems may improve using different methods. one of this methods is redundancy allocation problem. in this problem by adding redundant component to sub-systems under some constraints, the reliability improved. in this paper we worked on ...

In discrete k-center and k-median clustering, we are given a set of points P in a metric space M , and the task is to output a set C ⊆ P, |C| = k, such that the cost of clustering P using C is as small as possible. For k-center, the cost is the furthest a point has to travel to its nearest center, whereas for k-median, the cost is the sum of all point to nearest center distances. In the fault-t...

The proof of Theorem 1.1 uses a reduction from the Label-Cover(K,L) problem. Given an instance G = (U, V,E) of the Label-Cover(K,L) problem, we construct a k-regular hypergraphH. For each vertex v ∈ V , we add a corresponding “block” {0, 1}v of 2 vertices in H. We assign a p-biased weight to each vertex, with p = 1− 2 k − δ. For each pair of edges (u, v), (u, v′) ∈ E, we add a hyperedge on the ...

We generalize the O( dn 2 )-time (1 + )-approximation algorithm for the smallest enclosing Euclidean ball [2, 10] to point sets in hyperbolic geometry of arbitrary dimension. We guarantee a O ( 1/ 2 ) convergence time by using a closed-form formula to compute the geodesic α-midpoint between any two points. Those results allow us to apply the hyperbolic k-center clustering for statistical locati...