A sparse graph that preserves an approximation of the shortest paths between all pairs of
points in a plane is called a geometric spanner. Using range trees of sublinear size, we …

Sublinear time complexity is required by the massively parallel computation (MPC) model.
Breaking dynamic programs into a set of sparse dynamic programs that can be divided …

Packedness is a measure defined for curves as the ratio of maximum curve length inside
any disk divided by its radius. Sparsification allows us to reduce the number of candidate …

A well-known clustering problem called Density-Based Spatial Clustering of Applications
with Noise~(DBSCAN) involves computing the solutions of at least one disk range query per …

We call an objective function or algorithm symmetric with respect to an input if after
swapping two parts of the input in any algorithm, the solution of the algorithm and the output …

The importance of processing large-scale data is growing rapidly in contemporary
computation. In order to design and analyze practical distributed algorithms, recently, the …

Given a set of points P in the Euclidean plane, the classic problem of convex hull in
computational geometry asks to compute the smallest convex polygon C with the vertex set …