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# Questions tagged [euclidean-distance]

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### Efficient Method for Distance Comparison in Euclidean Space

I have a vector of 2D Euclidean coordinates, and I need to find out if two or more points are within a distance threshold. The naive approach is to compare each point with every other point, but I am ...
1 vote
24 views

137 views

### Algorithm for shortest continuous line to join N points

I have a set of points in a 2D plane. I'm searching for an algorithm that: Draws a continuous line passing through all the points starting from a random point. Optimizes for the minimum total line ...
90 views

### How to embed Pearson distance into Euclidean space

I have a lot of numerical vectors, each of dimension 1000. I would like to compare them according to their Pearson distance. This works fine but comparing all vectors to each other is quadratic time ...
464 views

### Algorithm to mimimally pair up points in 3D space

Given a set of $n$ points $P$ and a set of $n$ points $Q$ in 3 dimensional space, what's the fastest algorithm to uniquely pair points in $P$ with points in $Q$ so that the sum of the square of the ...
1 vote
936 views

### Computational complexity comparison of floating-point Euclidean distance calculation with binary fixed-point Hamming-distance calculation

This could relate to different applications, but my application of interest is in similarity-search systems based on high-dimensional feature vectors. In these systems, since search based on ...
147 views

### Splitting a set of points in the plane evenly and sorting it

Input: A set of points P(x,y). There are two versions of it - Px, sorted by x and Py, sorted by y. Output: The two even halves of Px, sorted by y. The trick here is that it has to work in linear ...
1 vote
301 views

### Total distance between points on a grid with time complexity lower than $O(n^2)$

I have $n$ points that form a grid with empty space and I need to find an algorithm that would calculate the total distance of those points with time complexity lower than $O(n^2)$. An example of a ...
I am in need of an algorithm for a part of a game (a mod) I am making. I have abstracted the problem: Given a 2D space with $N$ random points $p_1...p_n$, calculate the nearest neighbor of each of ...