The tag has no wiki summary.

learn more… | top users | synonyms

5
votes
2answers
759 views

Solve for $A$ and $B$ in $AXB=Y$

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 $\mathbb{R}$-linear ...
4
votes
0answers
234 views

Checking whether an element is in all inclusion-wise maximal common independent sets of two matroids

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) of $M$ and $M'$. It ...
18
votes
1answer
200 views

Decidability of equality of expressions built using 1,+,-,*,/,^

Consider expressions built using number $1$, arithmetical operators $+, -, *, /$ and exponentiation ^ (in case of multiple values, the principal value is assumed, the same way as it implemented in ...
6
votes
0answers
117 views

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
3answers
503 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
1answer
330 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
1answer
183 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
3answers
249 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
1answer
101 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
2answers
701 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
votes
2answers
88 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
1answer
129 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
1answer
302 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 ...
0
votes
0answers
94 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
votes
0answers
74 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
2answers
59 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
0answers
174 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
1answer
158 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 ...
1
vote
0answers
116 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
vote
0answers
109 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
1answer
277 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
2answers
584 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
1answer
141 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
votes
0answers
118 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 ...
1
vote
0answers
43 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
votes
5answers
759 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, ...
1
vote
1answer
253 views

Find root in finite field

What efficient algorithms exist for the solving $x^N = a$ in GF(q)? What are their complexities?
1
vote
1answer
269 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
0answers
186 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
votes
0answers
140 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 ...
1
vote
2answers
217 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
0answers
75 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
1answer
215 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
1answer
332 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 ...
0
votes
0answers
80 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
1answer
103 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
1answer
150 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
1answer
246 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 ...
7
votes
1answer
345 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
3answers
831 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
1answer
233 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
1answer
330 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
2answers
240 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
1answer
294 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
1answer
183 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 ...
4
votes
2answers
149 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
votes
3answers
521 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
2answers
175 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
votes
1answer
218 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 ...
3
votes
1answer
107 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 ...