Let $x_1,\ldots,x_N \in \{0,1\}^D$ be $N$ binary vectors in ${\mathbb R}^D$, assumed affinely independent. Is there an efficient algorithm for determining whether a new binary vect …

I have a homogeneous ideal $I=\langle f_1,\ldots,f_r\rangle$ of the polynomial ring $\mathbb C[X_1,\ldots,X_n]=:R$ where each of the $f_i$ is actually over $\mathbb Z$. My computat …

Let $R = \mathbb{Z}[x_{1}, \dots, x_{r}]$. Let $X$ be $n \times n$ matrix with entries in $R$. Let $Y$ be $m \times m$ matrix with entries in $R$ formed from $\mathbb{Z}$-linear or …

I'm trying to get my head around the maths used here: http://visualwebsiteoptimizer.com/ab-split-test-duration/ Can someone point me in the right direction in terms of what algor …

What is the Bahadur-Anderson Algorithm, and which book could one read to learn it?

When trying to develop an algorithm for a program, I got with the following problem: Determine the approximate location of $O$, if you can take finite samples $P_n$ from known loc …

We are given a graph $G=(V,E)$ with positive edge weights $w_{i}$ and numerical {0,1,-1} labels $l$ for all vertices . We know that $G$ has a subset $G'$ with all vertices labeled …

I believe the current lowest-memory algorithm for computing the $n^{th}$ binary digit of $\pi$ requires $O(log(n))$ bytes and $O(n^2 log(n))$ days (I pick Bellard over Bailey–Borwe …

Let a constant $B \ge 1$, and let $l_1 = 0$, $b_1 = 0$ be the values of $l$ and $b$ (respectively) at time $t = 1$. Let $l_{t+1} = l_t + 1$ if $b_i < B$, and $l_{t+1} = l_t$ ot …

Given two matroids $M$ and $M'$ over the same universe $E$, and some element $x \in E$, I am interested in the importance of $x$ for the intersection (the common independent sets) …

I was just shocked when I saw these consecutive outcomes of an L-system converging to the Sierpinski triangle (shown in the picture below). I'm interested to know how could one a …

Consider expressions built using number $1$, arithmetical operators $+, -, *, /$ and exponentiation ^ (in case of multiple values, the principal value is assumed, the same way as i …

Set D : Set of decision algorithms X∈D if and only if X is an Turing machine algorithm with finite length takes one input i, binary number X(i)=0 or X(i)=1 o …

A (simple, finite, connected) graph $G$ is distance regular if there exist integers $b_i,c_i,i=0,...,D$ such that for any two vertices $x,y$ in $G$ and distance $i=d(x,y)$, there a …

The problem of the complexity of the exact counting problem for primes is interesting. The best result we have about primes is that it is hard for TC0. But counting the number of w …