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Results tagged with algorithms
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user 126667
Informally, an algorithm is a set of explicit instructions used to solve a problem (e.g. Euclid's algorithm for computing the greatest common divisor of two integers). For more specific questions on algorithms, this tag may be used in conjunction with the approximation-algorithms, algorithmic-randomness and algorithmic-topology tags.
4
votes
Connecting $2n$ points in $\mathbb R^2$ with line segments s.t. each point belongs to exactl...
@RobPratt's answer describes a good general-purpose approach. The specific case where edge weights are given by Euclidean distances is also a well-studied problem. The paper A Divide-and-Conquer Algor …
- 25.2k
29
votes
Accepted
How does one find the "loneliest person on the planet"?
The paper Vaidya, Pravin M., An $O(n \log n)$ algorithm for the all-nearest-neighbors problem, Discrete Comput. Geom. 4, No. 2, 101-115 (1989), ZBL0663.68058 gives an $O(n \log n)$ algorithm for the " …
- 1,446
6
votes
Number of paths equal less than equal to a certain length
This problem seems to be NP-hard, in an informal sense. I'll sketch how we could use an algorithm for this problem to solve the knapsack problem. Suppose given $n$ objects with weights $w_1$, ..., $ …
- 25.2k
2
votes
Algorithmic Combinatorics resources?
The method of coupling from the past can be used to sample uniformly at random from certain distributions. Here is a simple demonstration which illustrates the method, and here it is in action comput …
- 25.2k
24
votes
Algorithm for finding the volume of a convex polytope
I think this problem is hard--the known algorithms are both slow and nontrivial to implement. See Exact Volume Computation for Polytopes for a survey. … An interesting feature is that there are various algorithms which are well suited for different kinds of polytopes.
As a practical answer, Qhull can compute volumes and surface areas. …
- 25.2k