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Mathematics

Questions tagged [algorithms]

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Mathematical questions about Algorithms, including the analysis of algorithms, combinatorial algorithms, proofs of correctness, invariants, and semantic analyses. See also (computational-mathematics) and (computational-complexity).

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I’ve been exploring a measurement approach for NP and NP-complete problems based on average time per logical step.I define:...
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MotivationI am experimenting with symbolic implementations of algorithms that, given a majorization relation between two exponent vectors, automatically generate Olympiad-style inequality proofs ...
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I have to randomly put $N$ points in a sphere of radius $R$ in a way that the distance of every point from the other points is greater than or equal to $r_0$. Is there an algorithm to solve this ...
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The greatest common divisor (gcd) of two integers $a$ and $b$ can be computed with the Euclidean Algorithm.With the gcd known, one can compute the least common multiple (lcm) via the formula $\mathrm{...
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Is there any better way than a brute force scan to find a square (or possible the smallest square) of format $A+n*B$, where $A$ and $B$ are some fixed constant integers? (I know that that is ...
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My question is about a certain combinatorial game. The game works as follows. We have $n$ urns, each of which contains $m$ balls, where $m$ and $n$ are positive and satisfy $m < n$. A move consists ...
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I have a DAG where every node has a (usually small) set of candidate integers. A candidate a is compatible with b if (a | b) or (b | a). For every root I want to choose one candidate per node to ...
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Given a graph, I wish to try and color it with the minimum number of colors (0,1...k).Each 2 connected vertices must have different colors.I proposed the following algorithm - Initialize an array of ...
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I'm trying to solve the following Codeforces question (https://codeforces.com/contest/837/problem/D), and I feel like I have a solution that's very close but is probably still over the time constraint....
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Problem: (from the Indian ZIO exam, $2021$, problem $2$)We are given a list of integers of length $n$. What is the minimum number of elements whose sign you need to flip such that every prefix sum ...
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As stated in title, I wonder know if there exists any algorithms for generating simplicial $n$-spheres on $k$ vertices.The motivation for seeking such algorithms comes from my goal to compute the ...
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I am unsure which category this question best fits into, so I apologize in advance if this is not the ideal place to ask.It is known (see for example:Do cyclic permutations of rows and column ...
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Consider the discrete Log Problem w.r.t. prime $p$. Given $b, p, r$ find $x$ where: $b^x\bmod p=r$.Q: What is the complexity of calculating the Least Significant Bit of $x$ in the worst case?Note: ...
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Let $K$ be any field. Two square matrices $A,B \in \text{Mat}_n(K)$ are called similar (denote it my $\sim$) iff there exists a $S \in \text{GL}_n(K)$ such that $A=SBS^{-1}$, so in this form an ...
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Consider the following streaming algorithm for maximum matching in a weighted graph....

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