# Tagged Questions

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### How was the $3x+1$ problem checked up to $5 \times 2^{60}$?

The Wikipedia article for the Collatz conjecture states that: The conjecture has been checked by computer for all starting values up to $5 \times 2^{60} \approx 5.764 \times 10^{18}$. It gives ...
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### Do most nonograms not require backtracking?

I get the impression that most Nonograms are "line solvable", meaning a computer never has to guess or backtrack. My understanding of this is that a tree searching algorithm isn't even necessary, ...
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### Is there a general algorithm to solve computable integral equation?

Hilbert's tenth problem ask for the general algorithm(finite number of operation) to solve of all Diophantine problems.Today, it is known that no such algorithm exists in the general case. What ...
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### algorithm for traversing a fractal in a “maximally ordered” way

consider a multidimensional fractal that can be "traversed" in an arbitrary order. is there an algorithm for traversing a fractal in a "maximally ordered" way? in other words the algorithm has ...
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### Finding the mathematical formula base on this C++ code

The code below is the solution to a ACM regional programming contest problem: Using credit cards for your purchases is convenient, but they have high interest rates if you do not pay your balance in ...
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### Mathematicly Untangeling Untangle.

I have a new addiction, I play Untangle to often, and i am wondering what is the mathematics behind it. some free games: (but be warned highly addictive) Javascript: ...
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### Maximum independent set problem

I need to study about the maximum independent set problem in graph theory. I need to study the $P_t$ free graphs and many other such variants and look up their maximum independent set characteristics. ...
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### looking for hypergraph decompositions

there are many thms for/types of graph decompositions. in contrast, am looking for various types of hypergraph decompositions...? also esp interested in graph analogs that translate somehow eg ...
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### Decision Making Algorithms - Chaos Theory

I'm doing research on decision making algorithms on robotics. And recently I've read a lot of about Chaos Theory. I've searched all over the web, in IEEEXplore, ACM Digital Library, but can't find any ...
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### Operational Research. (Ressource Management)

I am looking for a solution that i know exists already in the field of "Operational Research"... I Just can't put my finger on the name of the thing. An heuristic to solve a very common and simple ...
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### software to decide whether a 2-generator subgroup of PSL(2,R) is discrete/free

Gilman developed an algorithm with polynomial complexity that, given two elements in PSL(2,R), decides whether the group they generate is free/discrete or not. I was wondering whether anybody ever ...
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### Generalized Straight Skeleton

The straight skeleton of a polygon can be computed by having the edges of the polygon move inwards at a uniform constant speed. Is it useful to generalize this computation process by varying the ...
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### Test for equivalence of algebraic expressions

We are looking for the most efficient (most recent, or best) techniques to check if two algebraic expressions (elementary, Calculus-type functions) are equivalent (or if an expression is equivalent to ...
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### Square Root Algorithm

I would like an efficient algorithm for square root of a positive integer. Is there a reference that compares various square root algorithms? Thanks.
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### efficient summation of $\sum_{i=1}^{n}\sum_{j=1}^{n}\sum_{k=1}^{n}\sum_{l=1}^{n}A_{ij}A_{ik}A_{il}A_{jk}A_{jl}A_{kl}$

I want to find an efficient algorithm for calculating a sum of products with entangled indices. For example, $\sum_{i=1}^{n}\sum_{j=1}^{n}\sum_{k=1}^{n} A_{ij}A_{jk}A_{ki}$, where $A_{ij}$ is the a ...
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### Algorithm to generate single iterative formula from an arbitrary sequence of numbers.

The end goal is to be able to compress paragraphs of words into arbitrary formulae, where the formula is calculated by some software using algorithms. So, is it possible to generate arbitrary ...
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### Is there an efficient way to compute 2-separations of matroids?

Edit: Pointers to helpful references would also be appreciated, of course. The topic of matroids is a relatively new one for me and I don't personally know any experts of this subject. Thus, if I do ...
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### Books to understand the construction of all groups of a specific order

The algorithms introduced by Besche–Eick (1999) were used to construct (or count) the groups of order up to 2000 in Besche–Eick–O'Brien (2002), yet I find the algorithms somewhat inaccessible. How ...
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### Graph clique problem

I'm not sure to what degree this is a graph problem, and algorithms question, or what, but I'll give the setup: I have a simple undirected graph given in the form (for example) ...
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### Are there books on algorithms for architecture?

I need books on algorithms for organic/nonlinear and linear architect anyone recommend a book?
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### Difference between two sets of data points

I'm making a simple calibration of a z-stage, by measuring a number of points in one direction with a constant $\Delta$Z between each sample. Then I reverse the direction and measure the same number ...
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### Details about “fingerprinting” algorithms for groups?

where can I find details about "Fingerprinting" algorithms (to test whether two groups are non-isomorphic) "‘Fingerprinting’: For every group $G_1,…, G_r$ evaluate various isomorphism-invariant ...
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### What is a good reference for basic shape detection algorithms

I've been doing research for a presentation on computer vision, and right now I'm specifically researching shape detection. Since this is a math course and not a programming course, I'm only concerned ...
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### Algorithm to find all vertices exactly $k$ steps away in an undirected graph

This question may be better served at cs.SE, but I am not very familiar with CS lingo, so I'm hoping the maths community would be able to answer it as well... I have an undirected graph, and I am ...
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### Pollard-Strassen Algorithm

I'm aware that the Pollard-Strassen algorithm can be used to find all prime factors of $n$ not exceeding $B$ in $O\big(n^{\epsilon} B^{1/2}\big)$ time. This is really useful because I need to find all ...
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### For Maths Major, advice for perfect book to learn Algorithms and Date Structures

Purpose: Self-Learning, NOT for course or exam Prerequisite: Done a course in basic data structures and algorithms, but too basic, not many things. Major: Bachelor, Mathematics My Opinion: Prefer ...
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### Mathematics in the “ The Art of Computer Programming”

I don't know of this the right place to ask this type of question and hence I apologize (in advance) for any inconvenience. Here is my question: I have studied Concrete Mathematics by Knuth, Graham ...
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### Bounds on the gaps in a variant of polylog-smooth numbers.

Sorry for the long intro. I think the explanation motivates the question and puts it in context. But if you want to skip the story, then just move on to the grey boxes; they should contain enough ...
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### Number of operations in grade school algorithm for multiplying 577 and 423

Given 577 x 423 with grade school algorithm you calculate 577 x 3 = 1731 577 x 2 = 1154 577 x 4 = 2308 These are 3 multiplications of a number by a single digit. Then, you go on and add 1731 + ...
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### good resources for getting started with algorithms

I am reasonably mathematically competent and use algorithms regularly in computing, however I have started reading through 'introduction to algorithms' but find I need to understand a few more basics ...
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