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Results tagged with algorithms
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user 10446
Informally, an algorithm is a set of explicit instructions used to solve a problem (e.g. Euclid's algorithm for computing the greatest common divisor of two integers). For more specific questions on algorithms, this tag may be used in conjunction with the approximation-algorithms, algorithmic-randomness and algorithmic-topology tags.
3
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1
answer
402
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How "often" does LLL-reduction produce "optimal" result ? Is there condition (or informal un...
Consider some lattice in R^4 (C^4) or C^8.
Famous "lattice reduction" procedures (like LLL latice reduction)
produces some "reduced basis". However in general there results are not "the best reduced …
- 24.8k
4
votes
2
answers
1k
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diameter of Voronoi cell of the lattice ? What about R^n ? What about small n =2,3,4 ?What a...
Consider a lattice in R^n.
Consider Voronoi cell of it.
What is known about diameter ? About the shape ? What are good references ?
As far as I understand they are not easy to compute.
May be in s …
- 24.8k
1
vote
0
answers
198
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How to find closest point to restricted lattice on the plane ? ( m*h1 + n*h2, for 0<m,n<N)
Consider finite piece of lattice i.e. points of the form m*h1 + n*h2, for 0<m,n<N h1, h2 -some vectors. Consider some point "P" on the plane. How to find (m,n) such that m*h1 + n*h2 is closest to "P" …
- 24.8k
2
votes
2
answers
206
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how to find vertex of parallelotope closest to given point P in R^n ? (Or minimize quadrati...
What algorithms (except of brute force) can be suggested to find the closest vertex of paralleloptope to "P" ?
Is it NP ? …
- 24.8k
5
votes
2
answers
965
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Lattice reduction in R^3 (R^4) or what is fundamental domain for SL(3,Z) , (SL(4,Z)) ?
What are the algorithms to find such a lattice reductions ? …
- 24.8k
6
votes
1
answer
2k
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Closest vector problem (=nearest lattice point) is trivial for "reduced lattice" ?
Consider some lattice in R^n. Take some point "P" in R^n (which does not belong to this lattice in general). The problem is to find "nearest" lattice point. The problem is known NP-hard in general it …
- 24.8k
21
votes
5
answers
3k
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How can you find an integer coefficient polynomial knowing its values only at a few points (...
Example: How can you guess a polynomial $p$ if you know that $p(2) = 11$? It is simple: just write 11 in binary format: 1011 and it gives the coefficients: $p(x) = x^3+x+1$. Well, of course, this po …
- 24.8k
2
votes
5
answers
3k
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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, chipe2,.. …
- 24.8k
3
votes
2
answers
571
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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 ? …
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15
votes
4
answers
4k
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Algorithm to check is representation irreducible ? Algorithm to decompose the reducible one ?
Question 2 Given a representation of a finite group, what algorithms can be used to decompose it to the direct sum of irreducibles) ? …
- 24.8k
1
vote
0
answers
8
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Algorithms (or packages) to find recurrence relations for given sequence of q-polynomials?
Assume we have sequence of polynomials : $P_i(q)$ - each term is polynomial in $q$. (With integer coefficients, but hopefully it is not important).
We expect that there exists recurrence relation: $P_ …
- 24.8k