Graph theory is afundamental branch of mathematicsthat studiesnetworksconsisting of
nodes (vertices) and their connections (edges). Extensive research has been conducted on …

We study the reverse shortest path problem on disk graphs in the plane. In this problem we
consider the proximity graph of a set of $ n $ disks in the plane of arbitrary radii: In this graph …

Given a set P of n points in the plane, a unit-disk graph G_ r (P) G r (P) with respect to a
radius r is an undirected graph whose vertex set is P such that an edge connects two points …

A unit-disk graph G (P) of a set P of points in the plane is a graph with P as its vertex set such
that two points of P are connected by an edge if the distance between the two points is at …

Shortest path problems are among the fundamental problems in graph theory. It is folklore
that the unweighted single source shortest path (SSSP) problem in general graphs can be …

Let S be a set of n geometric objects of constant complexity (eg, points, line segments, disks,
ellipses) in R 2, and let ϱ: S× S→ R≥ 0 be a distance function on S. For a parameter r≥ 0 …

The expression of emotion in music performance is the soul of music, and the emotion
revealed by the performer during the performance can bring emotional resonance to the …

Given a set $ P $ of $ n $ points that are moving in the plane, we consider the problem of
computing a spanning tree for these moving points that does not change its combinatorial …

In this paper we study a few proximity problems related to a set of pairwise-disjoint segments
in {ℝ} ². Let S be a set of n pairwise-disjoint segments in {ℝ} ², and let r> 0 be a parameter …

We present several near-linear algorithms for problems involving visibility over a 1.5-
dimensional terrain. Concretely, we have a 1.5-dimensional terrain T, ie, a bounded x …