Abstract
Let S ⊂ R
2 be a set of n point sites, where each
s ∈ S has an associated radius rs > 0. The disk graph
D(S) of S is the graph with vertex set S and an edge
between two sites s and t if and only if |st| ≤ rs + rt,
i.e., if the disks with centers s and t and radii rs and
rt, respectively, intersect. Disk graphs are useful to
model sensor networks.
We study the problems of finding triangles and of
computing the girth in disk graphs. These problems
are notoriously hard for general graphs, but better
solutions exist for special graph graph classes, such
as planar graphs. We obtain similar results for disk
graphs. In particular, we observe that the unweighted
girth of a disk graph can be computed in O(n log n)
worst-case time and that a shortest (Euclidean) triangle in a disk graph can be found in O(n log n) expected
time.
2 be a set of n point sites, where each
s ∈ S has an associated radius rs > 0. The disk graph
D(S) of S is the graph with vertex set S and an edge
between two sites s and t if and only if |st| ≤ rs + rt,
i.e., if the disks with centers s and t and radii rs and
rt, respectively, intersect. Disk graphs are useful to
model sensor networks.
We study the problems of finding triangles and of
computing the girth in disk graphs. These problems
are notoriously hard for general graphs, but better
solutions exist for special graph graph classes, such
as planar graphs. We obtain similar results for disk
graphs. In particular, we observe that the unweighted
girth of a disk graph can be computed in O(n log n)
worst-case time and that a shortest (Euclidean) triangle in a disk graph can be found in O(n log n) expected
time.
| Original language | American English |
|---|---|
| Title of host publication | Proc. 33rd European Workshop on Computational Geometry, EuroCG 2017 |
| Pages | 205-208 |
| Number of pages | 4 |
| State | Published - 2017 |
Publication series
| Name | Proc. 33rd European Workshop Comput. Geom.(EWCG), |
|---|