# Questions tagged [euclidean-distance]

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### Find the placement of gates on 2D points that minimizes the total distance of all paths to be made

Suppose we have a 6 vertices graph. We also have 6 gates. Each gate is attributed a path. For example, Gate 'A' will have to go to 'B'- 'C' - 'D' and 'E' Gate 'B' will have to go to 'D' Gate 'C' will ...
53 views

### Scaling down a set of points into a smaller area

A visibility graph $G(P) = (V,E)$ of a set $P = \{p_1, \dots, p_n\}$ of points is defined as follows. Each vertex $u \in V$ corresponds to a point $p_u \in P$. There exists an edge $uv \in E$ if, and ...
47 views

### 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 ...
29 views

### Finding smallest triangle to fit all points

I'm supposed to find an algorithm that, given a bunch of points on the Euclidean plane, I have to return the tightest (smallest) origin centered upright equilateral triangle that fits all the given ...
55 views

### Cosine distance in a space, and cheating?

I read an example of using cosine distance in RGB space, and it pointed out that (eg.) dark red and light red have a cosine distance (CD) of zero because CD only gives you the angle between vectors ...
1 vote
11 views

### Finding overlapping time under distance condition

I have a set of records (2 or more for each person) on multiple peoples locations (latitude and longitude) with timestamps. each record has: person ID, latitude, longitude, timeStamp. for each 2 ...
1 vote
22 views

### Locality Sensitive Hashing for Sets

Are there locality sensitive hashes that work nicely with sets? Each set would get a hash, the order of the elements in the set does not change the hash, and sets that share more elements are closer ...
91 views

### Given a vector of points, what is the fastest algorithm to find all pairs of points at a distance of 1?

Given a vector of points (on the 2D plane), what is the fastest algorithm to find all pairs of points at a distance of 1? Of course, I could use the $O(N^2)$ algorithm to check all pairs of points. ...
1 vote
25 views

### Efficient intersection detection between disks with identical radius

I have a set of $N$ points randomly positionned on a rectangular space (btw with either absorbing, reflecting or wrapping boundaries), and I need to obtain the distances between every 2 points whose ...
1 vote
32 views

### Embedding from $L^\infty$ space to $L^2$ space

I have a set $X$ of $n$ points in a $poly(n)$-dimensional $L^\infty$ space. Does there exist a way to map the points into $poly(n)$-dimensional $L^2$ space so that the distances between points in $X$ ...
57 views

### A heuristic for finding the vector that is maximally distant from a set of vectors

I have two sets of vectors: A and B. I want to find the vector Bi in set ...
22 views

### Is it possible to approximate the cosine similarity by dot products?

My goal is to find an approximate way to calculate the cosine similarity by inner products. Before the question look at the image below taken from Improved Asymmetric Locality Sensitive Hashing (ALSH) ...
62 views

### Finding the smallest distance between a point and a set of points

I have a GPS dataset that corresponds to a route taken by a vehicle in a day. It consist of a set of coordinates. Then say I have a coordinate and I want to know how close this coordinate is to this ...
37 views

### Euclidean space vs metric space in density clustering algorithms

I'm trying to find out if these algorithm still work if i replace the Euclidean space with metric space defined on the input point set. But i'm having some trouble figuring it out for some of them. I ...
894 views

### Recovering a point embedding from a graph with edges weighted by point distance

Suppose I give you an undirected graph with weighted edges, and tell you that each node corresponds to a point in 3d space. Whenever there's an edge between two nodes, the weight of the edge is the ...
143 views

### Optimal Item Locations given Traversal Paths

I have a given fully-connected undirected graph associated with (known) distances or alternatively a distance matrix, where the nodes or matrix rows/columns represent locations. Additionally, I have a ...
71 views

### Mahalanobis distance of point to plane algorithm

I am trying to understand the Mahalanobis distance of a point from the plane given by this paper. The algorithm is given below: Calculate covariance of point $S_{uu}$ Apply a whitening transform to ...
1 vote
67 views

### Can we make at most 3 comparisons in the closest points algorithm instead of 7?

Let's say I am using the divide and conquer algorithm outlined here, but I only want to return the minimum distance. I understand why that algorithm puts an upper-bound at 7 but I think that can be ...
1 vote
32 views

### Show that the local feature size is Lipschitz continuous

In class we defined "local features size" $\rho$ as follows: Let $C$ be a smooth closed curve in the plane, and let $x$ be a point of $C$. The local feature size $\rho(x)$ of $x$ is the ...
49 views

### Distance from high dimensional convex hull to target point T

I have a set S of high dimensional points in Euclidean space, with convex hull H (not known); and some target point T in that space not in or on H. Rather than worry about calculating both H and the ...
76 views

### Why is it hard to show that the euclidean Steiner tree problem is in NP?

I read that for the euclidean Steiner tree problem it is known that it is NP-hard, but not known whether it is in NP or not. [Wikipedia] Shouldn't the euclidean version obviously be in NP since the ...
1k views

### expected pairwise square euclidean distance between points

How can I show that the expected pairwise square euclidean distance between points in $X$ is $Θ(d)$? Where $X$ is a $(x_1,...x_n)$ of points generated uniformly at random in the unit, d is d-...
37 views

### Finding multiple paths through a grid such that every grid square is equally used

Setup Here’s the setup: I have an $N$ x $N$ grid of tiles, and a list of $M$ agents that need to move across the grid. Each agent has its own start tile $S(a)$, end tile $E(a)$, and an exact number ...
31 views

### Efficient parameterization of low vertex count polygons

I'm trying to design a method to represent polygons as vectors. There are many ways to do this, but I have a few goals and I'm not sure what representation is best to fulfil these. The objectives are: ...
28 views

### Computing the minimum distance between each pain of points

I am trying to read an algorithm for computing minimum distance between each pair of points from the book: Algorithm Design Algorithm Design It considers the points in a line. If the points are in ...
122 views

### Approach for algorithm to find closest 3-D object in a list of many similar objects to a given test case

Lets say I have a list of many (10s of thousands - millions) objects, and each of these objects has a given number of 3-D vertices (my current implementation uses 8 vertices each, but this number can ...
149 views

### "Loneliest point" algorithm

Problem: I'm looking for an algorithm to find the maximal Euclidean distance between points in a set $R$ and another set $S \subseteq R$. Specifically, given a finite set of points $S$ in $n$-...
205 views

### Approximation algorithm to visit all nodes in an undirected, weighted, complete graph, with shortest sum of edge weights

I'm looking for an algorithm that gives a smallest value of 'travel cost' within the following constraints: a complete, connected, weighted graph, vertices are defined in 3d euclidean space, ...
1 vote
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1 vote
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### In multiobjective optimization, how to calculate the distance to reference point?

In multiobjective optimization, what does the distance exactly means, is it: 1) The distance from reference point (V) to an individual (Xi) (candidate solution) in the population (decision space). <...
144 views

### Clustering non-overlapping time series

I have thousands of times series of different length and different time. I want to group them together so that I know the optimal ones to pick as input for a ML algorithm and to document how they are ...
25 views

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### How to prevent overflow and underflow in the Euclidean distance and Mahalanobis distance

I was working in my project when I was struck by the question of whether it would be necessary, or at least cautious, prevent overflow and underflow in the calculation of these two distances. I ...
76 views

### How to detect intersecting segments based on length of the segments

As part of a larger problem, I am trying to detect based on the distance matrix which segments intersect in the original 2D space that originated the matrix. I don´t have coordinates (lat/long, x/y or ...