Questions tagged [euclidean-distance]
The euclidean-distance tag has no usage guidance.
57
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Finding the Point with Maximum Distance from the Boundary of a Closed Polygon in 2D Euclidean Space
Given a closed polygon defined in the 2D Euclidean plane. My objective is to determine the point within this polygon that is furthest away from its boundary. In other words, I want to find the point ...
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Finding shortest path between two points in a polygon whose vertices are given?
A contiguous single polygon is specified by it's vertices $(v_1, \ldots, v_n)$, given in order such that the line between $v_i$ and $v_{i+1}$ is an edge of the polygon (there's also an edge between $...
- 532
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Does T5 or another embedding embed every possible length tokenization?
I’m curious about an embedding technique where every possible “tokenization” of a text gets an embedding - not just individuals words, but every single 2-gram, 3-gram, and n-gram.
Does this exist?
Or ...
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Efficient ways to sort pairwise distances for set of points in Euclidean space?
Consider a Euclidean space $\mathbb{R}^d$. Consider $ X \subset \mathbb{R}^d$ where $X$ is a finite set with $|X|=n$. Consider the set of line segments $\{xy | x,y \in X\}$ . I have a process $Z$ that ...
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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 ...
- 113
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186
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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 ...
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211
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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 ...
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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
- 195
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53
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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 $X$ ...
- 315
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
- 121
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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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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 ...
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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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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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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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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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44
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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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2
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182
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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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151
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"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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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 ...
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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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41
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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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415
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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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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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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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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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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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776
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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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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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172
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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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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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117
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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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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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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 ...
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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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285
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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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427
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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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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) ...
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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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2
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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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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 ...
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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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