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# Questions tagged [algorithms]

Informally, an algorithm is a set of explicit instructions used to solve a problem (e.g. Euclid's algorithm for computing the greatest common divisor of two integers). For more specific questions on algorithms, this tag may be used in conjunction with the approximation-algorithms, algorithmic-randomness and algorithmic-topology tags.

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### Iterative algorithms for computing the kernel of a matrix

Suppose $A$ is an $m \times n$ matrix in the form $$A=\begin{pmatrix} — a_1 —\\ — a_2 —\\ \vdots \\?— a_m — \end{pmatrix}$$ where $a_i \in R^n$ is the $i$-th row of $A$. It is possible to determine ...
0answers
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### Practical calculation of minimum weight vertex-disjoint cycle covers

How are minimum-weight vertex-disjoint cycle covers of large dense symmetric graphs actually calculated in actual implementations? I know that the problem can be reduced to general matching by ...
3answers
116 views

### Fast computation of a ball with radius r with largest number of input points

We are given a set S of n points equipped with some metric and an integer $r>0$. We define $B(x,r) \subseteq S$ (the ball with radius r centered in x) to be the set of points in S within distance r ...
0answers
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### Correctly defining a grah problem [closed]

I would like to solve a graph theory problem but I am struggling finding the most efficient Algo to solve it because I'm not correctly defining it. Here is my problem: I have two sets of data: A={A1,...
0answers
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### Linear-algebraic simplification of the Smallest Grammar Problem

I don't get any people interested on MSE usually with this type of problem, and it is an untried idea. So I'm testing the waters out here. :) The smallest grammar problem problem once solved will ...
0answers
83 views

### Computing the number of topologies on a finite set [duplicate]

Denote by $T(n)$ the number of non-homeomorphic topologies on a set with $n$ elements. I recently noticed that I am not aware of any good way of computing $T(n)$. Is there an interesting lower bound ...
0answers
74 views

We are given a set $S$ of $n$ points in $\mathbb{R}^d$ and a (hidden) vector $\mathbf{w}\in\mathbb{R}^d$, where each point $\mathbf{v}\in S$ is associated with a binary label equal to the sign of $\... 3answers 355 views ### Given$N$integers on a circle, how to choose them in pairs to obtain minimum sum? (Added by YCor 2019 July 7): it has been mentioned in the comments that this is part of a contest "Circular merging, July Challenge 2019 Division 1", where an equivalent question (just more clearly ... 2answers 103 views ### Algorithm to list all Kostant partitions Let$\Phi_+$be the set of positive roots in some root system, and let$Q_+$be the positive part of the root lattice, i.e., the set of elements of the form$\sum_{\beta\in \Phi_+}m_\beta\beta$with$...
1answer
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### Jordan Decomposition of Sparse matrix

Suppose we are given $n \times n$ rational matrix, $A$ with at most $k$ nonzero elements in each row and each column with $k \ll n$. What is the best algorithm to compute its Jordan decomposition? ...
0answers
45 views

### Calculating Minimum Spanning Trees in Very Big Graphs

I need to determine Minimum Spanning Trees (MST) of very big complete graphs, whose edgeweights can be calculated from data that is associated with the vertices. In the planar euclidean case, for ...
1answer
52 views

### Intersection of sphere with triangle containing moving vertices

First off, apologies if I cannot properly articulate my question in the most formal way. However, I believe my question should be simple enough to grasp anyhow. In $\mathbb{R}^3$, I would like to ...
0answers
17 views

### Difference Between Total Least Squares Plane and Plane Orthogonal to Principal Axis of Inertia Tensor

Given a finite set $P$ of points in $\mathbb{E}^3$ , one can calculate an approximating plane either as the solution of a Total Least Squares problem or by interpreting the problem physically, ...

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