All Questions
7 questions
9
votes
3
answers
2k
views
Embedding planar graphs into the grid
I've seen the following lemma in a paper. The result is by Valiant.
A planar graph $G$ with maximum degree $4$ can be embedded in the plane using $O(|V|)$ area in such a way that its vertices are at ...
- 903
7
votes
1
answer
760
views
Difference Sets
Suppose
$$
P \subseteq \{1,2,\dots,N\},\quad |P| = K
$$
We calculate the differences as: $$d=p_i-p_j\mod N,\quad i\ne j$$
Now let $a_d$ denote the number of occurrence of $d$ (for $d = 1, 2, \dots , N ...
- 123
4
votes
1
answer
1k
views
Algorithm for the shortest path through all the points of a 2D cloud
I have an array of points with their coordinates X and Y. Each point represents a bus stop.
I need to sort the points in a sequence by giving them sequence numbers, so that the path from the first to ...
- 61
4
votes
2
answers
219
views
Algorithm for grouping tetrahedra from Voronoi diagram
I have a set of 3D Voronoi generator points and their neighbouring points, which, when connected, should result in a Delaunay tetrahedralization. However, I'm having a hard time implementing this. My ...
- 142
3
votes
1
answer
58
views
Wheel-graph with minimal spoke-weight sum centered at a planar-euclidean point
Questions:
Given a set $\mathcal{P}$ of points in the Euclidean plane, what is the complexity of finding for a given point $p_i$ inside the convex hull $\mathrm{CH}\left(\mathcal{P}\right)$ the set $\...
- 13.2k
3
votes
0
answers
111
views
Is there a Havel-Hakimi for geometric graphs?
Suppose that we are given $n$ points in the plane, with a degree prescribed for each, and the question is whether we can place a geometric graph on them. Is there an efficient algorithm for this?
...
- 19k
1
vote
0
answers
79
views
Touring a sequence of convex polygons with minimal energy
There is a known problem of touring a sequence of $n$ polygons: given a starting point $s$, an ending point $t$ and a sequence of polygons $P_1,\dots,P_k$ with a total of $n$ vertices, find points $...
- 177