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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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      Distinct sums for edge weights

      For each $n\geq1$, consider a special tree with $2n+1$ nodes which are assigned values $a_i$ from the set $\{0,0,1,2,3,\dots,2n-1\}$. Only $0$ can be a repeated assignment. The edges are only the ...
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      Algorithm to determine if a rational fraction has only non negative coefficients

      Is there an algorithm that takes as input a polynomial in two variables $P \in \mathbb{N}[x,y]$ and outputs YES if and only if the coefficients of the series $\frac{1}{1-(x+y)} - \frac{1}{1-P}$ are ...
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      Is it possible to construct an algorithm for determining the polynomial or system of polynomials of an algebraic variety?

      Algebraic varieties, roughly speaking, are set of solutions of a system of polynomials over a finite number of real or complex variables (algebraically closed field). Now consider we have a computer ...
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      Enumerating all edge-disjoint shortest paths from “s” to “t”

      Given: An edge-weighted directed graph $G$ A start vertex $s$ A target vertex $t$ I want to enumerate all edge-disjoint shortest paths from $s$ to $t$, in ascending order of path length. So, as an ...
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      Traveling Salesman Problem on finite group

      Given a finite group $H$, define a norm on $H$ to be a function $f : H \rightarrow \mathbb{R}_{\geq 0}$ satisfying: $f(x) = 0 \iff x = e$ is the identity; $\forall x \in H$, we have $f(x) = f(x^{-1})$...
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      45 views

      Algorithm for checking positive definite matrix over a subspace

      There is an algorithm that for any input matrix $A \in \mathbb{R}^n$ satisfies $x^\top A x>0$ for all $x \in \mathbb{R}^n$, e.g. by using Cholesky algorithm. Is there an algorithm that, for matrix $...
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      71 views

      Finding Elusive Orbits in GL action on polynomials

      I am attempting to generate orbit representatives for the action of $\operatorname{GL}(n, F_2)$ on homogeneous polynomials of fixed degree $d$ in $n$ variables using random methods. However, some ...
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      Weighted vertex coloring of hypergraphs

      Let $G=(V,E)$ be a simple graph. Let $w$ be a non-negative, integer valued weight function on the vertex set. The chromatic number $\chi(G,w)$ of the vertex-weighted graph $(G,w)$ is defined to be ...
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      1answer
      47 views

      Algorithm generating digraphs

      Is there an algorightm generating all digraphs with $n$ edges up to isomorphism whose underlying graph is not a tree? For example, for $n=3$, there are only two such digraphs, representable as $\text{...
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      86 views

      Algorithm to compute the convex hull of a set of $m$ possibly intersecting convex polygons in the plane

      I am trying to find an algorithm to compute the convex hull of a set of $m$ possibly intersecting convex polygons in the plane, with a total of $n$ vertices. Let $h$ denote the number of vertices on ...
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      74 views

      Generating Machin Type formulas with inverse hyperbolic tangents for logarithms

      Machin Type formulas for $\pi$ have the following general form: $$c_{0} \frac{\pi}{4}=\sum_{n=1}^{N} c_{n} \arctan \frac{a_{n}}{b_{n}}$$ Recently browsing through this question here, I really became ...
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      27 views

      Succinct circuits and NEXPTIME-complete problems

      I am fascinated by a recent fact I was reading: Succinct Circuits are simple machines used to descibe graphs in exponentially less space, which leads to the downside that solving a problem on that ...
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      44 views

      Fastest Algorithm to calculate Graph pebbling number?

      I am interested in Graph Pebbling, and in particular what are the fastest known algorithm is to find the pebbling number of a graph. Also, i am interested whether there are lower limits on the runtime ...
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      26 views

      Algorithms for Detecting the Completion of a Triangle in a Stream of Edges

      I need to efficiently determine in a complete weighted graph $G$ the sequence of triangles according to descending order of circumferences. My idea would be to incrementally construct a new graph $...
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      73 views

      How to efficiently sample uniformly from the set of $p$-equipartitions of an $n$-set?

      I have a question related to this one. For $n,p \in \mathbb{N}_+$ such that $p\mid n$, let $\mathcal{P}^{\rm eq}$ be the set of all equipartitions of $n$ in $p$ sets; i.e., in sets of equal size $\...

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