Questions tagged [euclidean-distance]

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1answer
28 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 ...
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0answers
23 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 ...
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0answers
25 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: ...
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1answer
20 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 ...
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2answers
50 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 ...
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0answers
111 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 $n$-...
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0answers
23 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 ...
2
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1answer
68 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, ...
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1answer
30 views

Closest k points - performance on large lists

Very similar to this Problem formulation: Given a list $L$ of n points with GPS coordinates and a second list $Q$ of $m$ points, find the $k$ (let's say 3) closest points on $L$ for each element on $...
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0answers
243 views

Stable and fast computation of the squared euclidean distance matrix

Let's say I want to compute the matrix $M$ of the squared euclidean distances between each pair of vectors $(x, y)$ belonging to two sets $X$ and $Y$ respectively. The sets of vectors $X$ and $Y$ have ...
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0answers
173 views

Sub-optimal and fast solutions to assignment problem

I am looking for a fast solution to the assignment problem for large cost matrices (5000x5000 or larger). The Hungarian algorithm is $O^3$, which is impractical for any moderately large problem. Are ...
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1answer
483 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-...
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1answer
265 views

In most locality sensitive hashing implemensions of SimHash, why is the cosine distance used and not the euclidean distance?

In Chapter 3 of Mining of Massive Datasets, the basis of locality sensitive hashing is explained. They notably mention simhash for the cosine distance, where random hyperplanes are generated, and for ...
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1answer
59 views

Comparison between: Maximum Absolute Difference & Min Steps in Infinite Grid

There are two questions that I am trying to draw a comparison between: ...
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1answer
395 views

Finding Euclidean Minimum Spanning Tree

Given a set of point $P$. Find the euclidean minimum spanning tree where each points is equally distributed on the plane using randomization. We can solve this problem with Prim's algorithm in $O(n^2)...
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0answers
23 views

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). <...
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94 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 ...
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0answers
22 views

Partial TSP in Euclidian plane

I'm interested in the following variant of Travelling Salesman Problem sometimes called Partial TSP. I'm particulary interested in the euclidian version : Input : A set $\{x_1,\dots,x_n\}\subset \...
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1answer
86 views

Counting arrays with Euclidean distance at most 2 from a given binary array

I have a binary array like this: $$A = [0,1,0,0,1,0]\,.$$ I'm trying to find a way to calculate how many arrays of the same length exist that have a Euclidean distance of 2 or less from this array. ...
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1answer
76 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 ...
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2answers
628 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 ...
2
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1answer
77 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 ...
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0answers
102 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 ...
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1answer
142 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 ...
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0answers
136 views

Is it possible to simulate/emulate non-euclidean geometry using computer graphics?

I am aware of the frequent use of "smoke and mirrors" in order to achieve the effect of non-euclidean geometry, but I was wondering it if it possible to implement spherical (sometimes called elliptic) ...
3
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1answer
117 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 ...
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2answers
1k views

All nearest neighbor in a changing 2d euclidean space

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 ...
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1answer
69 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 ...
3
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1answer
97 views

Should planar Euclidean graphs be planar straight-line graphs?

An Euclidean graph, by definition is A weighted graph in which the weights are equal to the Euclidean lengths of the edges in a specified embedding and a graph is called planar if it can be ...
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2answers
2k views

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 ...
3
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1answer
419 views

Efficient algorithm to fulfil a set of coordinate constraints

I have a set of labelled points and a set of distance constraints between pairs of points, consisting of a lower and upper distance bound. There is definitely an arrangement of the points in 3D space ...
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1answer
2k views

Finding nearest of a list of points on Euclidian plane to a given reference point

Problem formulation: Given a list $L$ of $n$ points in the Euclidian plane and a reference point $R$ also in that plane, find a closest point $P\in L$ such that, for all $X\in L$, $|PR|\le|XR|$. ...
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0answers
109 views

How fast is closest pair?

I'm reading a recent paper "Finding Correlations in Subquadratic Time, with Applications to Learning Parities and the Closest Pair Problem" by Gregory Valiant on finding approximate closest pairs in $...
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0answers
16 views

Modifying the Erroneous Pairwise Distances of 4 Points to Get Coplanarity

Consider four points $i,j,k,l$ and their pairwise Euclidiean distances $d(ij)$ $d(ik)$ $d(il)$ $d(jk)$ $d(jl)$ $d(kl)$ Say that, we know the coordinates of the points $j$, $k$ and $l$. However, we ...
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1answer
189 views

Can the Euclidean distance function be computed using only XOR's

The Eulidean distance function $d$ of $x$ and $y$ is given by: $ d(x,y)=\sqrt{x^2-y^2} $ Let us assume that $x$ and $y$ are fixed-point numbers, or $x,y$ are element of some subfield $f_n$ of $F_p$. ...
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4answers
735 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 ...