Clustering problems often arise in the fields like data mining, machine learning etc. to group a collection of objects into similar groups with respect to a similarity (or dissimilarity) measure.… (More)

We study a natural extension of the Maximum Weight Independent Set Problem (MWIS), one of the most studied optimization problems in Graph algorithms. We are given a graph G = (V,E), a weight function… (More)

Voronoi game is a geometric model of competitive facility location problem played between two players. Users are generally modeled as points uniformly distributed on a given underlying space. Each… (More)

We revisit two NP-hard geometric partitioning problems – convex decomposition and surface approximation. Building on recent developments in geometric separators, we present quasi-polynomial time… (More)

We consider the following metric clustering problem. We are given two point sets X (clients) and Y (servers), and a metric on Z = X ∪ Y . We would like to cover the clients by balls centered at the… (More)

The clustering problem, in its many variants, has numerous applications in operations research and computer science (e.g., in applications in bioinformatics, image processing, social network… (More)

Given an initial placement of a set of rectangles in the plane, we consider the problem of finding a disjoint placement of the rectangles that minimizes the area of the bounding box and preserves the… (More)