arXiv subjects
Publications and source records attributed to Sima Hajiaghaei Shanjani.
In this paper we study the following problem: Given $k$ disjoint sets of points, $P_1, \ldots, P_k$ on the plane, find a minimum cardinality set $\mathcal{T}$ of arbitrary rectangles such that each rectangle contains points of just one set $P_i$ but not the others. We prove the NP-hardness of this problem.
A communication network is a graph in which each node has only local information about the graph and nodes communicate by passing messages along its edges. Here, we consider the {\it geometric communication network} where the nodes also occupy points in space and the distance between points is the Euclidean distance. Our goal is to understand the communication cost needed to solve several fundamental geometry problems, including Convex Hull, Diameter, Closest Pair, and approximations of these problems, in the asynchronous CONGEST KT1 model. This extends the 2011 result of Rajsbaum and Urrutia for finding a convex hull of a planar geometric communication network to networks of arbitrary topology.