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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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        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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        41 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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        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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        71 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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        54 views

        Algorithm to find “islands” in sparse matrices

        I am playing with a weird dataset of ternary images (+1,0,-1 values only) which happen to be very sparse (avg. > 90%). I would like to determine the most relevant "islands" (or should I call them ...
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        206 views

        Is this kind of “Gerrymandering” NP-complete?

        [I posted this on math.stackexchange.com about two weeks ago, but didn't get any reply, so I'm trying it here.] Consider the following simplified form of "Gerrymandering": You have $n^2$ squares ...
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        49 views

        Algorithm to find the minimal number of multiplications

        Start with the $\mathbb{Q}$-vector subspace $V_0$ of the polynomial ring $Q[x_1,\ldots,x_n]$ spanned by $\{1,x_1,\ldots,x_n\}$. In each step, we can choose an element of the form $v_iv_i'$ for $v_i,...
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        Cycle types of permutations from affine group

        Let $V$ be a vector space of dimension $n$ over the field $F=\mathrm{GF}(2)$. We identify $V$ with the set of columns of length $n$ over $F$. Let $G = \mathrm{AGL}(V)$ be a group of affine ...
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        Limit Behavior of a Graph Iteration

        ,Let $G(V,E)$ be a weighted complete graph. Let further $\min_k(v_i)$ denote, depending on whether the context is arithmetic or set theoretic, either the set of the $k$ smallest edges adjacent to $...
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        62 views

        Algorithms for the explicit matrix isomorphism problem over $\mathbb{C}$

        Suppose that $A$ is a $d^2$ dimensional algebra over $\mathbb{C}$ and we know the multiplication tensor $c_{ij}^k$ and the unit $u^k$ in some basis. If $A$ is semi-simple and has a single simple ...
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        When is MAXCUT “easy”?

        MAXCUT is NPC but is known to be polynomial for, say, planar graphs. Are there any other graph families where it is known MAXCUT is polynomial? (Please don't say "bipartite graphs" :) )
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        Finding the minimum sum of a subset of entries of a given matrix with combinatorial constraints

        Given a matrix $M\in\mathbb{N}^{n\times n}$, let $Z$ be the set of all the $M$'s entry subsets $S$ such that (i) no two entries of $S$ are on the same row or column of $M$ and (ii) $|S|=n$. Clearly we ...
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        1answer
        99 views

        Randomized Algorithm for finding maximum in a sequence

        I read it on some website (which I do not remember now) that in a sequence of length $n$, to find the maximum value (with high probability) one only needs to generate a constant multiple of $\log(n)$ ...
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        Treewidth problem equivalence

        Say we are solving a tree decomposition problem, e.g. given a graph $G = (V, E)$ we try to find a chordal graph $H$ such that $V(H) = V(G)$, $E(G) \in E(H)$ and the maximal clique in $H$ is minimal ...
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        2answers
        208 views

        Procedure to determine the equality of numbers in rationals plus square root

        Consider the set $\mathbb{Q}^\sqrt{}$ of real numbers that can be constructed by applying finitely many of the five operations $+$, $-$, $\cdot$, $/$ and $\sqrt{}$ to a positive rational number. ...

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