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Results tagged with geometric-probability
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user 6094
6
votes
Length of nearest neighbor path in travel salesman problem
A careful experimental analysis of the nearest-neighbor (NN) heuristic (among other heuristics) is described in this paper:
Johnson, David S., and Lyle A. McGeoch. "The traveling salesman problem: …
- 151k
4
votes
The Largest Piece of Circumference
To re-ask Pietro Majer's question, what do you mean by a "piece of circumference"?
$20$ random points, $n=10$ chords.
If you mean the largest section of the circumference c …
- 151k
3
votes
Density of a saturated random packing of congruent circles
Following user @j.c.'s lead, here is another paper on RSA (Random Sequential Adsorption), which concludes with a density of $0.77$. From the abstract:
Hinrichsen, Einar L., Jens Feder, and Tor …
- 151k
2
votes
What is the probability that these sets intersect?
Not an answer. Just wanted to see what your set $A$ looks like in $\mathbb{R}^3$:
Set $A$ for $d = 0.6$ in origin-centered unit cube.
- 151k
1
vote
Alignment of random points
This is not an answer to your original specific question, but
this recent related result (and its references) may help:
"Finding Points in General Position."
Vincent Froese, Iyad Kanj, André Ni …
- 151k
1
vote
Accepted
The consequence of overlap sharing for the length-distribution of rods randomly placed on a ...
This is not an answer, only a simplification and conjecture concerning that simplification.
First, only consider $N$ large enough so that the interval/circle is fully covered
(the "eventually" in my c …
- 151k
1
vote
Complexity of Random Delaunay Triangulation in 3D
You may gain some empirical insight from this exploration:
Tanemura, Masaharu. "Statistical distributions of Poisson Voronoi cells in two and three dimensions." FORMA-TOKYO- 18, no. 4 (2003): 221- …
- 151k