We study the convex-hull problem in a probabilistic setting, motivated by the need to handle
data uncertainty inherent in many applications, including sensor databases, location-based …

In this paper we study the all-pairs shortest paths problem in (unweighted) unit-disk graphs.
The previous best solution for this problem required O (n^ 2 log n) time, by running the O (n …

One of the longest-standing open problems in computational geometry is bounding the
complexity of the lower envelope of n univariate functions, each pair of which crosses at …

Let D be a set of n pairwise disjoint unit disks in the plane. We describe how to build a data
structure for D so that for any point set P containing exactly one point from each disk, we can …

Sorting an array of n elements represents one of the leading problems in different fields of
computer science such as databases, graphs, computational geometry, and bioinformatics …

Let ${R}=\{R_1, R_2,..., R_n\} $ be a set of regions and let $ X=\{x_1, x_2,..., x_n\} $ be an
(unknown) point set with $ x_i\in R_i $. Region $ R_i $ represents the uncertainty region of …

In this paper we study how to efficiently order a set of imprecise points. In one dimension, the
order of a set of points is their sorted order from low to high. A set of imprecise points in the …

Finding the coordinatewise maxima and the convex hull of a planar point set are probably
the most classic problems in computational geometry. We consider these problems in the …

We study the diameter of a spanning tree, ie, the length of its longest simple path, under the
imprecise points model, in which each point is assigned its own occurrence region instead …

Entering the era of big data, human beings are faced with an unprecedented amount of
geometric data today. Many computational challenges arise in processing the new deluge of …