All Questions
8 questions with no upvoted or accepted answers
17
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Splay trees and Thompson's group $F$
( I apologize for only indicating some easy to find references, but new users are not allowed to link more than five). This is very speculative, but:
Question: Is there a reformulation of the Dynamic ...
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9
votes
0
answers
2k
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Exactly Counting the Number of Lattice Points in an $n$-Dimensional Sphere
Let $S_n(R)$ denote the number of lattice points in an $n$-dimensional "sphere" with radius $R$. For clarification, I am interested in lattice points found both strictly inside the sphere, and on its ...
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4
votes
0
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155
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Effective "almost enumeration" of monotone boolean functions
Denote by $\mathcal{M}(n)$ the set of all monotone functions $\{0,1\}^n \to \{0,1\}$.
Can $\mathcal{M}(n)$ be represented as $\mathcal{M}(n) = \{ f(t) | t\in \{0,1\}^k \}$ such that:
1) $k = \log |\...
- 2,576
4
votes
0
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73
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Is the $d$-dimensional Arrangement of Trees still $NP$-hard?
The $d$-dimensional Arrangement Problem for general graphs is known to be $NP$-hard since the special case $d=1$ (OLA) already is (Garey et al, [1976]). For Trees however, the one dimensional case can ...
- 41
2
votes
0
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245
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Pancake sorting problem – Is computing f(n) NP-hard?
The so-called Pancake flipping problem first discussed by Jacob E. Goodman here yields two entangled problems:
MIN-SBPR (Sorting By Prefix Reversals) - Given a permutation, find the smallest sequence ...
- 51
1
vote
0
answers
157
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Indecomposability of image transformations (pure algebra). Open questions
W-transformations -- definitions
We will consider a class called finite window transformations $\ T:C^\mathbb Z\rightarrow C^\mathbb Z\ $ defined a paragraph below; $\ \mathbb Z\ $ is the ring of ...
- 7,500
1
vote
0
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576
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Minimizing quadratic form over permutations
Let $Q$ be an $n \times n$ real symmetric matrix and $x$ an $n \times 1$ real vector. Consider the following minimization problem:
$\min_{\pi \in S_n} ~(\pi x)^{\rm T} Q (\pi x)$,
where $S_n$ ...
- 1,839
0
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59
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NC0 randomness vs. non-uniformity
In
Ajtai and Ben-Or. A theorem on probabilistic constant depth
Computations. STOC '84, 1984
Ajtai and Ben-Or show a non-uniform derandomization of BPAC0.
Is there a similar relation known for ...
