Questions tagged [exp-time-algorithms]
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71 questions
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Are there any candidate languages in NE but not E?
Let ${\bf E}=\text{DTIME}(2^{O(n)})$ and ${\bf NE} = \text{NTIME}(2^{O(n)})$
Is there any candidate natural language being in ${\bf NE} \setminus {\bf E}$, that is, people believe is ${\bf NE}$ but ...
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Calculation on Sparsification and critical clauses in SAT
I followed from this question.
I need to prove, the final result $s_k \leq (1 − \Omega(k^{−1}))s_{\infty}.$
But before prove the final result first I need to prove the $s_k \leq (1 − d/k))s_{\infty}$.
...
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Sparsification and critical clauses in SAT
I have been studying the Exponential-Time Hypothesis, ETH, from this paper, there defined $s_k = \inf\{\delta \geq 0 | k\text{-}SAT \in RTIME[2^{\delta n}]\}$.
But in that paper's page number 10, I ...
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What is the fastest algorithm for computing exact network reliability?
In the network reliability problem, we are given an undirected graph $G$ on $n$ vertices and a parameter $p\in (0,1)$, and are tasked with determining the probability that $G$ becomes disconnected (i....
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What are some examples of decidable Natural Problems outside of EEXP?
I haven't really seen any examples of problems in complexity classes higher then EEXP. What are some examples of some primitive recursive problems outside of EEXP? Ideally with a large number of Es, ...
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Space complexity of quantum algorithms for Subset sum
As far as I can find there are several quantum algorithms for the Subset sum problem with $2^{n/3}$ running time. Is there an algorithm with $2^{n/3}$ running time that uses much less space?
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Minimum vertex-separators under edge addition
I am trying to prove the following claim.
Let $T$ be a minimum $st$-separator in an undirected graph $G$, and let $x \in T$.
Let $S\neq T$ be a minimal $st$-separator (i.e., not necessarily minimum), ...
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Best known algorithm for NEXP-complete problem
What is the best (in time) algorithm for NEXP-complete problems?
Is there an algorithm that solve a NEXP-complete problem in time $2^{o(2^n)}$?
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Algorithmically determining proof complexity for Frege systems?
I apologize if this falls wildly short of research level - I am just learning the very basics of proof complexity and lack any real logic background.
Let $F$ be a Frege proof system (a finite complete ...
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Fastest Known Algorithm to Count Acyclic Orientations in a Graph
Given an undirected graph $G$, an acyclic orientation of $G$ is choice of orientation for each edge of $G$ (turning each edge into an arc) such that the resulting directed graph has no directed cycles....
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Fastest Known Algorithm for $k$-Dimensional Matching and $k$-Exact Cover
Given a $k$-uniform hypergraph $G$ (i.e., each edge of $G$ contains precisely $k$ vertices) on $n$ vertices, the $k$-Exact Cover problem is the task of deciding if there exists $n/k$ edges in $G$ ...
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anything hinting that EXPTIME $\subseteqq$ PSPACE?
Anything or evidence hinting that $$EXPTIME \subseteqq PSPACE$$？
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Problems that started out with hopelessly intractable algorithms that have since been made extremely efficient
This is somewhat of a meta-cstheory question, and is more historical in nature. What are some good examples of problems for which the literature followed the develpment below:
The original algorithms,...
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If $\sf{E} = \sf{NE}$. Then $\sf{NP}-{P}$ contains no sparse sets [closed]
I am reading "The Complexity Companion" by Hemaspaandra & Ogihara, I have a question about lemma 1.21.
In its proof, they suppose $L$ is some sparse language in $\sf{NP}$ ($||L^{=n}||&...
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On $\text{ETH}$ with $m$ as parameter: consequences of algorithm running in time $2^{\delta m}$ where $\delta \to 0$ as $k \to \infty$
It has been shown in [1] that $k\text{-SAT}$ has a $2^{o(n)}$ algorithm if and only if it has a $2^{o(m)}$ algorithm, $n$ being the number of variables and $m$ being the number of clauses.
Being $s_k=\...
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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 ...
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Does two-sided error have more capability than one-sided error?
From $P=RP$ extrapolation we might think $EXP=REXP$.
What evidence do we have $BPP\subseteq REXP$?
What consequence $REXP\subseteq BPP$ gives other than what $EXP\subseteq BPP$ gives?
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NP-hard problems with very fast exponential-time algorithms
NP-hard problems with very fast exact exponential-time algorithms, say with $O(1.01^n)$ time, are very rare.
Is any fact like
"For any constant $\epsilon>0$ there is an NP-hard 'natural' ...
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What is the fastest known algorithm for computing a 1.99-approximation of Vertex Cover?
It is known that computing $(\sqrt 2 -\epsilon)$-approximation for VC is NP-hard and that UGC implies that even a $(2 -\epsilon)$-approximation is hard.
There is also a parameterized algorithm for ...
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Correctness of AKS algorithm for shortest vector problem
Short question
In the end of section 1 of Regev's notes about the AKS algorithm for SVP, why is the following true?
for each such $i$,$y_i− x_i$ remains $w$ with probability $1/2$ or otherwise ...
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A question about UE
Much has been written about the class UP see related (even more in literature)
example question here. Much is understood about the class UP, and its place in collapsing the PH too. UP has a played ...
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Asymptotic time required to simulate a Turing machine M for k steps
Problem: Given an encoding of a Turing machine M and a natural number k as input, find the output of M (given a blank tape) after k steps.
Wikipedia's page on EXPTIME-complete says it takes O(k) time ...
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Question on deduction that a certain problem requires exponential space
My question concern's a statement from the classic paper The equivalence problem for regular expressions with squaring requires exponential space.
Regular expressions with squaring are like ordinary ...
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The problem of deciding whether a monotone CNF implies a monotone DNF
Consider the following decision problem
Input: A monotone CNF $\Phi$ and a monotone DNF $\Psi$.
Question: Is $\Phi \to \Psi$ a tautology?
Definitely you can solve this problem in $O(2^n \cdot \...
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Why is it a mystery if PSPACE ?= EXPTIME?
It seems obvious to me that $PSPACE \neq EXPTIME$. I, however, do not believe that my seemingly obvious logic would not be picked up by more intelligent people if it was so simple, so I'm assuming ...
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Most general setting for fine-grained exponential-time complexity classes?
Consider the class of functions computable in time $(b+o(1))^n = 2^{\log_2{(b)} \times n + o(n)}$ on a $2$-tape Turing machine.
By the Hennie-Stearns theorem, the same functions are computable in ...
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Proof: PTIME not equal EXPTIME [closed]
Can someone give me the name of a paper where this is proved or maybe just prove it here (if it's easy enough)?
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Reference for a circuit lower bound for slightly superexponential time
It is known that $EXP$ doesn't have circuits of size $n^k$. On the other hand proving $10 n$ lower bound on circuit size for $E$, $NE$ or even $E^{NP}$ is a known open problem.
My question is ...
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Oracle comparing $EXP$ with $UP$
Heller (Theorem 6) gave an oracle relative to which $NP=EXP$, and Homer & Selman gave an oracle relative to which $P=UP$ and $\Sigma_2^P=EXP$.
Beigel, Buhrman, Fortnow (freely available author's ...
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Is it possible to approximate Maximum Independent Set in $O(2^k\text{poly}(n))$ time?
We know that MIS is hard to approximate within a $n^{1-\epsilon}$ factor in polynomial time and that it is $W[1]$-hard and thus unlikely to admit a $f(k)\text{poly}(n)$ time exact algorithm. (here, $k$...
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Intermediate problems between PSPACE and EXPTIME
Intermediate problems between P and NP are quite famous, and are sometimes considered as complexity classes by themselves.
Do you know of any problem that is known to be PSPACE-hard and in EXPTIME, ...
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Reference request: complexity of $k$-partite $k$-SAT
Let's consider following variation of $k$-SAT that I will call $k$-partite $k$-SAT:
given $n$ variables that are divided into $k$ groups and a $k$-SAT formula $\phi$ such that each clause has literal ...
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Parameterized Algorithm to Speed up Exact Exponential-time Algorithm
The connection between $c^kn^{O(1)}$ for $c<4$ and exact exponential-time algorithms beating brute-force $O(2^n)$ algorithms has been known for a long time. However, when $c\geq 4,$ there are not ...
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Consequences of faster parameterized integer programming
Integer programming in $k$ variables can be done in $k^{O(k)}$ time and $O(k^c)$ space.
Is there any consequence if it can be done in $k^{O(k^\alpha)}$ time and $O(k^c)$ space for some $\alpha\in(0,1)...
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Is there a W[1]-hard problem that can be solved in $2^{o(n)}$ time?
This question is about subset problems (the solution is a subset of the instance, so trivially enumerable in $2^n \cdot n^c$ time), and the parameter is the solution size, so-called the standard ...
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EXP-Complete Problems vs Subexponential Algorithms
Does the fact that a problem $A$ is EXP-time complete implies that $A$ is
not in $DTIME(2^{o(n)})$?
I'm aware that by the time hierarchy theorem, $EXP=DTIME(2^{n^{O(1)}})$ is not
included in $E=...
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Do any quantum algorithms improve on classical SAT?
Classical algorithms can solve 3-SAT in $1.3071^n$ time (randomized) or $1.3303^n$ time (deterministic). (Reference: Best Upper Bounds on SAT )
For comparison, using Grover's algorithm on a quantum ...
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Questions regarding SETH
I read about the strong exponential time hypothesis, which states (as far as I understand) that SAT problem cannot be solved in running time $O(2^{\epsilon n})$ for any $\epsilon < 1$, where $n$ is ...
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Problems with Unknown Single Exponential Time Agorithms
I'm looking for examples of problems for which it is easy to get algorithms running in time $2^{O(n\log n)}$, or $2^{O(n^c)}$ for some $c>1$ but for which it is not known whether there is an ...
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Two DFA intersection emptiness connections to SETH & L vs P
(re "fine grained complexity") Wehar has proved that
Two DFA intersection emptiness in $O(n^{2-\epsilon})$ time → SETH false.
does anyone see any particular key proof difficulty, challenge, ...
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Complexity of validity problem for Monadic First Order Logic?
Monadic First Order Logic is FOL with no function symbols, and predicate symbols restricted to arity 1. For this question, let's say that the = symbol is also forbidden. I want to know the complexity ...
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Approximate matching in table of integer vectors
Disclaimer: This is my first question on cstheory.stackexchange.com so please be forgiving.
I have a list of M (M is big, more than 1 million elements) vectors of integers. Each vector can contain 0-...
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Information about algorithm to generate sequences
I want to make an application for generating a sequence (called S) of items (I), based on conditions (called C).
The Conditions are defined as a property with a 'bonus/reduction'. The total score (T) ...
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What is the evidence for average case separation between EXP and NEXP?
There is significant evidence from cryptography that there exist NP-complete problems that are hard in the average case (meaning that e.g. $AvgP \nsupseteq DistNP$). Namely, we have candidate one-way ...
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Is MAX-SAT SETH (like) hard?
If we make a random assignment to the variables in $k$-sat ($m$ clauses), we are going to satisfy $(1-2^{-k})m$ clauses in expectation. In general satisfying fewer clauses is considered easy.
There ...
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Finding exact value with a quotients of products of random values
Sorry for the haphazard title: really not sure what this should be called
Suppose we have a set of $z$ random values $S = r_1, \dots, r_z$ drawn from $\mathbb{Z}_N$ (where $N$ is some large prime).
...
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What is the worst-case runtime complexity to transform a NFA to DFA via Rabin-Scott's power set construction?
What is the worst-case runtime complexity to transform a NFA to DFA via Rabin-Scott's power set construction? Why?
Details:
http://en.wikipedia.org/wiki/Powerset_construction states that the worst-...
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Examples of problems where exponential algorithms run faster than polynomial algorithms for practical sizes?
Do you know of any problems (preferably at least somewhat well known), where, for a practical problem size, an exponential algorithm runs much faster than a best-known polynomial time counterpart.
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Examples of $2^{\Theta(n^2)}\text{poly}(n)$-time algorithms
What are notable examples of problems for which the best currently known algorithm has $2^{\Theta(n^2)}\text{poly}(n)$ running time ?
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Example of context-free grammar that triggers exponential behaviour without memoization in RD parsers
It is often said that memoization brings the complexity of recursive-descent parsers
from exponential to polynomial. However, I had a hard time finding an example grammar
that triggers the exponential ...
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