Graph theory is a fundamental branch of mathematics that studies networks consisting of
nodes (vertices) and their connections (edges). Extensive research has been conducted on …

We revisit a classical graph-theoretic problem, the single-source shortest-path (SSSP)
problem, in weighted unit-disk graphs. We first propose an exact (and deterministic) …

We prove a structural theorem for unit-disk graphs, which (roughly) states that given a set of
unit disks inducing a unit-disk graph and a number, one can partition into subsets such that …

We initiate the study of diameter computation in geometric intersection graphs from the fine-
grained complexity perspective. A geometric intersection graph is a graph whose vertices …

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

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 …

In this paper, we present an algorithm for computing a feedback vertex set of a unit disk
graph of size $ k $, if it exists, which runs in time $2^{O (\sqrt {k})}(n+ m) $, where $ n $ and …

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 …

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 …