The algorithms tag has no wiki summary.

**7**

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### How quickly can we test if a graph is distance-regular?

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 are exactly $c_i$ ...

**3**

votes

**3**answers

812 views

### L-systems and Sierpinski Triangle

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 arrange the rules of ...

**3**

votes

**1**answer

345 views

### Fastest Digit Extraction for Any Irrational Number

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–Borwein–Plouffe for ...

**0**

votes

**1**answer

224 views

### Giving a general term of a recursive function, and upper bound for it

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 $l_{t+1} = l_t$ otherwise
Let ...

**2**

votes

**3**answers

275 views

### existence of equivalence checking algorithm

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 or X(i) runs ...

**1**

vote

**1**answer

115 views

### Separation of Anti-Hole Inequality

Given an undirected graph $G=(V,E)$ with no loops or multiple edges, a stable set is a set of vertices for which no two vertices are adjacent.
An induced subgraph $H$ of $G$ is called an odd-antihole ...

**6**

votes

**2**answers

779 views

### Approximate number of primes below a given integer?

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 witnesses to a TC0 ...

**0**

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**2**answers

97 views

### Fitting algebraic expression to a number [algorithm]

I know that it may turn out useless, but this is precisely the reason why I'm asking.
Does any one know of an existing piece of code that would find me the best approximation to a given irrational ...

**3**

votes

**1**answer

150 views

### Using Fourier Transform to speed up calculation of forces following an inverse square law

Suppose I have $n$ electric point charges in, say, two dimensions. Is there any algorithm (and I have a hunch that it might be related to the Fourier transform) to compute the net forces that act on ...

**2**

votes

**1**answer

361 views

### At what point does Miller-Rabin become faster than trial division?

I've read in various places (and know) that Miller-Rabin is a much faster primality test than trial division for large $N$, but is much slower than trial division for small $N$.
My question is: how ...

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**0**answers

115 views

### max*min/(max+min) vs max*min/(max-min)

While working on a genetic algorithm, I needed to devise a fitness function for each chromosome. Each chromosome has 2 attributes: maximum accuracy and minimum accuracy.
The fitness should increase ...

**0**

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**0**answers

87 views

### Maximal Zero Sums Partition

You are given $n$ numbers between $-n$ and $n$, the sum of numbers is $0$. Divide the given sequence on disjoint subsequences in such a way that each subsequence has zero sum. Each element should ...

**0**

votes

**2**answers

62 views

### Maximize 2-tuple efficiently

Hello I am lookin for an algorithm that efficiently finds all Tuples ${(x,y)$$\varepsilon U|\forall (u,w) \epsilon U \rightarrow (x>=u \vee y>=w)$.
I could of course check all tuples against ...

**3**

votes

**0**answers

214 views

### (Co)limit computations for diagrams of Vector Spaces

Fix a field $K$ and consider a finite directed graph $\Gamma$ where multiple edges between a pair of vertices are allowed so long as the total number of edges is finite. Associate to each vertex $v$ a ...

**2**

votes

**1**answer

181 views

### Reducing the error of Algorithms by assigning variables formulas instead of values

Let me first give the intuition for my question: Suppose that you want to use a ruler to mark $n$ points in a line on a page, with 1 cm distance between neighbor points. There are two ways:
1- Mark ...

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**0**answers

126 views

### regular hyper graph construction

Is there any algorithm to generate 3-uniform k-regular hypergraph with n vertices?? Any help is appreciated. Thanks.

**1**

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**0**answers

144 views

### Optimize a convex hull on a 2D histogram so the selected points match a target shape

I have an image (can be 2D or 3D), and compute a 2D histogram of the image (for example, the pixel intensity and gradient along certain direction). There is a known target region $R^*$ in the image. I ...

**2**

votes

**1**answer

494 views

### Removing cycles from an undirected connected bipartite graph in a special manner

Consider an undirected connected bipartite graph (with cycles) $G = (V_1,V_2,E)$, where $V_1,V_2$ are the two node sets and $E$ is the set of edges connecting nodes in $V_1$ to those in $V_2$. We ...

**9**

votes

**2**answers

603 views

### When polynomial f(x^2) can be factored as g(x)·g(-x) ?

In relation to my question Expression for the sum of square roots of zeros of a polynomial
How to characterize polynomials $f(x)$ with rational coefficients such that $f(x^2)=g(x)\cdot g(-x)$ where ...

**2**

votes

**1**answer

189 views

### algorithmic almost equitable partitioning

Let $G$ be a graph -- possibly infinite, but I will be glad to learn a positive result even in the finite case. Then the trivial partition (i.e., one cell coinciding with the whole $G$) is clearly ...

**0**

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**0**answers

123 views

### Find polynomial in finite field

We have $A$, $B \in GF(q^k)$
We want to find polynomial $h \in GF(q)[x]$ where
$h(A) = B$
What is the lowest degree of $h$?
How to find $h$ with the lowest degree and what is complexity of this ...

**2**

votes

**0**answers

47 views

### Most efficient algorithm for computing norm of the residual for the least squares problem in the rank deficient case

I have a large $m\times n$ data matrix $A$, $m>n$, and response $m$-vector $b$. I need to calculate $E = ||Ax-b||_2$ as quickly as possible, where $x$ is the least squares solution. I don't need ...

**2**

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**5**answers

1k views

### Algorithm to solve Sokoban-like game on graphs - move chips from one set of vertices to another

The question is close to the Sokoban game (thanks to Dima Pasechnik !), but a little different in details.
Consider a directed graph (multi-graph). Consider some set of marked chips (chip1, ...

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vote

**1**answer

333 views

### Find root in finite field

What efficient algorithms exist for the solving $x^N = a$ in GF(q)?
What are their complexities?

**1**

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**1**answer

273 views

### calculate function from its divizor

There is elliptic curve $C (y^2 = x^3 + Ax + B)$ over $GF(q)$.
There is algebraic function f on C.
We have div(f).
How calculate f as rational function ( $f = (f_1(x) + yf_2(x)) / (g_1(x) + ...

**2**

votes

**0**answers

189 views

### Choosing a base where a given digit of a given number appears the most times

Is there an algorithm for choosing a base where a given digit of a given number appears the most times, that works better then trial and error? (see also this)

**0**

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**0**answers

162 views

### Condition and algorithm for Decomposition of formal power series

$$F(x)= \Sigma_0^{\infty} a_i x^i$$ is formal power series, $a_i\in N\bigcup 0$,N is the set of natural number,under what condition may it be decomposed into a system of equations terms of which are ...

**0**

votes

**2**answers

262 views

### Enlcosing a set of ellipses within one ellipse

Hello,
Is there an algorithm that takes in a set of ellipses and gives back and ellipse that encloses the set?

**1**

vote

**0**answers

93 views

### Toroidality testing

Is there a standard test for the recognition of toroidal graphs?
I have been using the Boyer-Myrvold algorithm (which has a MATLAB implementation) and would like to know if there is something ...

**4**

votes

**1**answer

253 views

### Generating non-isomorphic graphs by adding edges to a given graph

Hello!
This question is in a way related to the one I posted on math.se. Since the question there did not produce any final answer I am trying my luck here!
I am given a fairly large graph $G$ and ...

**6**

votes

**1**answer

394 views

### Is equality of terms for “real” numbers with roots, logarithm, exponential, sin, cos, and other trigonometric operations decidable with a Turing-machine?

If yes, how? Also, I know you can't do it for arbitrary statements about real numbers, but that's not what I'm asking, and by "real" numbers, I mean the numbers constructible from 1, -, /, and the ...

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124 views

### Examples of applications that use the Schnorr digital signature?

Hi there. It may not be the best place to ask this question, but here goes:
I have made a study on digital signatures, especially on the Schnorr digital signature, and I was just wandering if there ...

**3**

votes

**1**answer

106 views

### Search for common substructures in list of graphs

I have had the following problem on several occasions and I was wondering whether there is a general technique to solve this problem.
Given a list of graphs with property $P$. Is there a general ...

**0**

votes

**1**answer

158 views

### An Algorithm to Determine a probable profit

I 'm searching for an algorithm (and except the naive brute force solution had no luck) that efficiently ($O(n^2)$preferably) does the following:
Supposing I’m playing a game and in this game I’ll ...

**2**

votes

**1**answer

294 views

### Finding a subspace disjoint from a union of subspaces

Let $k$ be a finite field (I care about $\mathbb F_p$, especially $\mathbb F_2$) and let $V_1,...,V_N\subset k^n$ be subspaces.
I want to find a subspace $S\subset k^n$ such that $S\cap V_i=0$ for ...

**12**

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**1**answer

510 views

### Constructive proof of “Projective implies proper”

For every ring $A$, the structural morphism of schemes $\pi_A : {\bf P}^n_{A} \to {\rm Spec}{A}$ is a closed map. The usual proof of this fact is not constructive : given equations of a closed subset ...

**16**

votes

**3**answers

850 views

### Easy functions ?

Let $f$ be an analytic function, and suppose that we want to compute
$f(x)$. The input consists of the digits of $x$ and the output of
a rational number approximating $f(x)$. A function $f$ is called ...

**6**

votes

**1**answer

271 views

### How do you compute the primes of bad reduction?

Suppose that I am given a subscheme $Y$ of $\mathbf{P}^n_{\mathbf{Z}}$, flat over $\operatorname{Spec}\mathbf{Z}$ and with smooth generic fiber $Y_{\mathbf{Q}}$, defined by the vanishing of some ...

**4**

votes

**1**answer

442 views

### Exact arithmetic for real algebraic numbers

There was a reply to a question (that I can't find) which mentioned SARAG (Some Algorithms
in Real Algebraic Geometry) see http://perso.univ-rennes1.fr/marie-francoise.roy/bpr-ed2-posted2.html. This ...

**0**

votes

**2**answers

324 views

### Creating composite rank [closed]

Problem: Suppose that $K$ different students are ranked based on $N$ different parameters (such as Physics marks, English marks, Biology marks, IQ etc). The rank under each parameter can be repetitive ...

**7**

votes

**1**answer

326 views

### Experimental mathematics: how are floating point equations discovered/converted to exact equations?

the 2005 AMS article/survey on experimental mathematics[1] by Bailey/Borwein mentions many remarkable successes in the field including new formulas for $\pi$ that were discovered via the PSLQ ...

**2**

votes

**1**answer

229 views

### An optimization problem, non complete bipartite graph and hungarian algorithm

I have two tables at my disposal, one work dataset and one reference dataset. Each dataset has got two columns, lets say these are fields A and B. I would like the rows in reference dataset with the ...

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**2**answers

153 views

### Computing Slim Extensions representing Ext

Hey Everyone
Let $A$ be an algebra over a field (group rings $k[G]$ for group cohomology, the Steenrod Algebra). We want to compute, say, $Ext_A(k,k)$, so let $F_*\to k$ be an $A$-free resolution. ...

**0**

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**1**answer

705 views

### Largest subarray with average $\geq$ k

I try to solve this problem. The algorithm I developped has a complexity of $O(n^2)$. When dealing with large data the program is brought to its knees. Do you have any idea that might be faster than a ...

**0**

votes

**2**answers

183 views

### Maximizing number of factors contributing in the sum of sorted array bounded by a value

I have a sorted array of integers of size n. These values are not unique. What I need to do is : Given a B, I need to find an i<A[n] such that the sum of ...

**6**

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**1**answer

245 views

### Is it possible to decide in polynomial time if a poset is a subposet of another which is given ?

I am reading some theory on partial orders and I wonder something which perhaps has a simple answer : Given two partial orders $G_1,G_2$ (by their hasse diagrams), is it possible to know in ...

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votes

**1**answer

111 views

### Median-of-k elements

Hello,
Assume I am given a sequence of $n$ elements (by sequence I mean an ordered set). I want to randomly pick $k$ elements out of these $n$ elements, where $k$ is an odd number $\leq n$.
Then out ...

**2**

votes

**1**answer

257 views

### Complexity of establishing finite groups (non)-isomorphism ?

Question Given two finite groups G and H of the same order N what are the algorithms and what is their complexity (in terms of N) to check is G isomorphic to H or not ? Is there polynomial in N ...

**10**

votes

**4**answers

2k views

### Algorithm to check is representation irreducible ? Algorithm to decompose the reducible one ?

Question 1 Given a representation of a finite group, what algorithm can be used to check is it irreducible or not ?
(Main case - complex numbers, comments on other cases are also welcome. "Given" ...

**2**

votes

**2**answers

264 views

### Lattice reduction on an orthonormal lattice?

Suppose you are given an inner product on a vector space and given a set of linearly independent vectors, and that you have been promised that the lattice they span has an orthonormal basis. Can you ...