Questions tagged [euclidean-distance]

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141 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 ...
2
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0answers
51 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 ...
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0answers
13 views

What's the best way to combine multiple A* searches?

I have a graph that looks like this The highlights nodes must be visited, and the blue node must be visited last, the stickman must be the start of the path. The weights are the Euclidean distance ...
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0answers
61 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 ...
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0answers
28 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 ...
2
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1answer
39 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 ...
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1answer
32 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 ...
2
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0answers
32 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 ...
2
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0answers
28 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: ...
0
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1answer
22 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
88 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 ...
2
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0answers
143 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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40 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
120 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
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1answer
33 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 $...
3
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0answers
296 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 ...
2
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0answers
194 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 ...
3
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1answer
738 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-...
1
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1answer
318 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
72 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
577 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
24 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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116 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 ...
2
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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
91 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. ...
2
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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
763 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
80 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
133 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 ...
3
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1answer
187 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 ...
3
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0answers
140 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
123 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 ...
2
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2answers
2k 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 ...
5
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1answer
70 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
107 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 ...
3
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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
441 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 ...
2
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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 $X\in L$, $|PR|\le|XR|$. ...
3
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0answers
110 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 ...
2
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1answer
230 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 $F_p$. ...
10
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4answers
793 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 ...