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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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        Doing Pareto via Khachiyan without weighted objective

        It seems Khachiyan proves polynomial time algorithm for LP using theorem 6.4.9 here in https://www.zib.de/groetschel/pubnew/paper/groetschellovaszschrijver1988.pdf which states: 'Any one of the ...
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        67 views

        Box stacking problem

        Real world problem alert: I am moving from my house to another one, and the problem below arised when I tried to fit some little boxes of various shapes into a large box: We are given a positive ...
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        76 views

        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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        28 views

        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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        40 views

        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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        238 views

        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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        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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        1answer
        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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        1answer
        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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