Questions tagged [succinct]
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22 questions
4
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Optimal encoding of a polytope's integer points
Question
Given a fixed $n\in\mathbb{N}$, weights $(w_i) \in \mathbb{R}_+^n$, and upper bound $B > 0$, I am looking for an optimal encoding of vectors $(e_i) \in \mathbb{N}^n$ that obey the ...
- 145
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2
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269
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Encoding of nodes in Binary Decision Diagrams
A straightforward implementation of Binary Decision Diagrams (BDDs) typically requires 12 bytes per node, with an additional 4 bytes commonly used for auxiliary data. Each node is encoded as a 4-tuple ...
2
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0
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232
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Can an $n$-element subset of a $2n$-element set be stored in $2n - \omega(1)$ bits?
There are $\binom{2n}{n} = \frac{4^n}{\sqrt{\pi n}} \cdot (1 - o(1))$ possible $n$-element subsets of a $2n$-element set. Therefore, any data structure storing such a set must use at least $2n - O(\...
- 2,412
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Is there a succinct representation of factoring which remains computationally intractable?
I'm looking for a succinct version of the factoring problem: i.e. given integers N and k, does N have a prime factor less than k, but somehow the input takes exponentially fewer bits to input? Ideally ...
- 403
3
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Succinct problems over uniform computational models
For a language $\Pi$, the traditional definition of "Succinct-$\Pi$" is the set of encodings of circuits whose truth tables are members of $\Pi$.
This definition is essentially restricted (...
- 1,244
5
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122
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Data structures to store monotone functions
I am looking for approaches storing strictly increasing natural-valued functions defined on a (subset of) $[0..N]$:
$$
\forall x \in X: 0 \le x \le N\\
f: X \to \mathbb N\\
\forall x,y\in X:\quad x<...
- 151
3
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1
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218
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CNF encoding of set cover - NExpTime-completness
Notation: given a CNF formula A over variables X, we write $[A(X)]$ for the set of valuations $v: X \to \{0,1\}$ such that $A(X/v)$ is true, i.e. the set of valuations that makes formula A true.
I ...
2
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0
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205
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Time complexity of Succinct-CVP
I want to know what is the best known lower time complexity of Succinct-CVP?
The succinct version of many P-complete problems are EXP-complete and Succinct-CVP is EXP-complete too (It is because of ...
- 220
15
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505
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Is there a P-complete language X such that succinct-X is in P?
I came across a paper called "A Note on Succinct Representation of Graphs". It seems that in the discussion section they claim that for any problem $X$ that is $\mathrm{P}$-hard under projections, $\...
- 5,317
4
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A succinct version of permanent that is $EXP$-complete
Succinct version of permanent is $NEXP$-hard (https://eccc.weizmann.ac.il/report/2012/086/) and so unlikely to be $EXP$-complete.
Permanent mod $2$ is in $\oplus L$ and so succinct version is ...
- 13.8k
6
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1
answer
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On succinct $EXP$ and $NEXP$ complete problems?
We know succinct version of many $P$-complete problems are $EXP$-complete. There are standard ways to define $EXP$-complete graph problems from succinct representations of these $P$ complete problems. ...
- 13.8k
1
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0
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198
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Information theoretic lower-bound on object graph serialization
This might be a daft quesstion, but here comes. I became intriqued about data serialization formats and tried to look for research on what could be the information theoric lower bound on encoding ...
- 111
10
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223
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Is there a counting complexity class for succint problems?
Encoding NP-complete problems succintly often makes them NEXP-complete. I am wondering if counting the number of solutions to such a problem with a succint encoding would be any harder than solving ...
- 833
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113
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What is the name of this data structure? (hash table with a limit on the number of entries)
Denote $[n] \triangleq \{1,2,\ldots,n\}$.
Assume we would like to have a data structure $S$ which kinda works as a dictionary from $[k]$ to $[v]$, and supports add/remove/update/query functionality, ...
- 9,608
6
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Practical algorithms for finding small arithmetic circuits
I have a multivariate integer polynomial $f : \mathbb{Z}^n \to \mathbb{Z}$ given as either as a circuit or as a list of monomials. I am interested in practical (though obviously exponential time) ...
- 3,298