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Approximating the Influence of a monotone Boolean function in O(√(n)) query complexity
[article]

2011
*
arXiv
*
pre-print

We study

arXiv:1101.5345v1
fatcat:la5grhg2tbd4bk5cd5kwbhdvri
*the*problem*of**approximating**the*total*influence**of*a*monotone**Boolean**function*=1 f: {±1}^*n*⟶{±1}, f: ^*n*→, which we denote by I[f]. ... We present a randomized algorithm that*approximates**the**influence**of*such*functions*to within a multiplicative factor*of*(1±) by performing*O*(√(*n*)*n*/I[f](1/))*queries*. ... A Lower Bound*In*this section we prove a lower bound*of*Ω √*n*I[f ]·log*n*on*the**query**complexity**of**approximating**the**influence**of**monotone**functions*. ...##
###
Approximating the Influence of Monotone Boolean Functions in O(√n) Query Complexity

2012
*
ACM Transactions on Computation Theory
*

We study

doi:10.1145/2382559.2382562
fatcat:qfookvmparhxtfrrg234jlhsf4
*the*problem*of**approximating**the*total*influence**of*a*monotone**Boolean**function*f : {0, 1}*n*→ {0, 1}, which we denote by I[f ]. ... We present a randomized algorithm that*approximates**the**influence**of*such*functions*to within a multiplicative factor*of*(1 ± ) by performing*O*√*n*I[f ] poly(1/ )*queries*. ... A Lower Bound*In*this section we prove a lower bound*of*Ω √*n*I[f ]·log*n*on*the**query**complexity**of**approximating**the**influence**of**monotone**functions*. ...##
###
The Query Complexity of Certification
[article]

2022
*
arXiv
*
pre-print

Our main result is a new algorithm for certifying

arXiv:2201.07736v2
fatcat:nt4dle3glnd23kvd5mmln7fhcu
*monotone**functions*with*O*(k^8 log*n*)*queries*, which comes close to matching*the*information-theoretic lower bound*of*Ω(k log*n*). ... We study*the*problem*of*certification: given*queries*to a*function*f : {0,1}^*n*→{0,1} with certificate*complexity*≤ k and an input x^⋆, output a size-k certificate for f's value on x^⋆. ... Acknowledgments We thank*the*STOC reviewers for their useful comments and feedback. Guy, Caleb, and Li-Yang are supported by NSF CAREER Award 1942123. Caleb is also supported by an NDSEG fellowship. ...##
###
Graphical Models: Queries, Complexity, Algorithms

2020
*
Symposium on Theoretical Aspects of Computer Science
*

Graphical models (GMs) define a family

doi:10.4230/lipics.stacs.2020.4
dblp:conf/stacs/CooperGS20
fatcat:rqyjypnqozd47frmaobbcpo5ei
*of*mathematical models aimed at*the*concise description*of*multivariate*functions*using decomposability. ... We restrict ourselves to*functions**of*discrete variables but try to cover a variety*of*models that are not always considered as "Graphical Models", ranging from*functions*with*Boolean*variables and*Boolean*...*The*best known general algorithm for*Boolean*submodular*function*minimization is*O*(en 3 log*O*(1)*n*) [82] . ...##
###
Query Complexity of Derivative-Free Optimization
[article]

2012
*
arXiv
*
pre-print

A distinctive feature

arXiv:1209.2434v1
fatcat:ne47u4bjyneprdfnhljafdm6my
*of**the*algorithm is that it uses only*Boolean*-valued*function*comparisons, rather than*function*evaluations. ... We also show that regardless*of*whether DFO is based on noisy*function*evaluations or*Boolean*-valued*function*comparisons,*the*convergence rate is*the*same. ...*Query**complexity**of**the**function*evaluation oracle E f ( x T ) − f (x * f ) ≥ c*n*σ 2 T 1 2 where*the*infimum is taken with respect to*the*collection*of*all possible estimators*of*x * f using just T*queries*...##
###
Efficient Inference for Complex Queries on Complex Distributions

2014
*
International Conference on Artificial Intelligence and Statistics
*

We consider problems

dblp:conf/aistats/DworkinKX14
fatcat:l4asmhfobrcrngopofjklpe43i
*of**approximate*inference*in*which*the**query**of*interest is given by a*complex*formula (such as a formula*in*disjunctive formal form (DNF)) over a joint distribution given by a graphical ... We give a general reduction showing that (*approximate*) marginal inference for a class*of*distributions yields*approximate*inference for DNF*queries*, and extend our techniques to accommodate even more*complex*...*The*absolute errors*of*each*approximation*are plotted as a*function**of**the*size*of**the*input layer*n**in*Figure 1 . Each data point represents an average over 25 trials. ...##
###
How Low can Approximate Degree and Quantum Query Complexity be for Total Boolean Functions?

2014
*
Computational Complexity
*

*In*this paper we study

*the*case

*of*

*approximate*degree and bounded-error quantum

*query*

*complexity*. ... It has long been known that any

*Boolean*

*function*that depends on

*n*input variables has both degree and exact quantum

*query*

*complexity*

*of*Ω(log

*n*), and that this bound is achieved for some

*functions*. ...

*FUNCTIONS*WITH QUANTUM

*QUERY*

*COMPLEXITY*

*O*(log

*n*/ log log

*n*)

*In*this section we exhibit two

*n*-bit

*Boolean*

*functions*whose bounded-error quantum

*query*

*complexity*(and hence

*approximate*degree) is

*O*(log

*n*...

##
###
How Low Can Approximate Degree and Quantum Query Complexity Be for Total Boolean Functions?

2013
*
2013 IEEE Conference on Computational Complexity
*

*In*this paper we study

*the*case

*of*

*approximate*degree and bounded-error quantum

*query*

*complexity*. ... It has long been known that any

*Boolean*

*function*that depends on

*n*input variables has both degree and exact quantum

*query*

*complexity*

*of*Ω(log

*n*), and that this bound is achieved for some

*functions*. ...

*FUNCTIONS*WITH QUANTUM

*QUERY*

*COMPLEXITY*

*O*(log

*n*/ log log

*n*)

*In*this section we exhibit two

*n*-bit

*Boolean*

*functions*whose bounded-error quantum

*query*

*complexity*(and hence

*approximate*degree) is

*O*(log

*n*...

##
###
How Low Can Approximate Degree and Quantum Query Complexity be for Total Boolean Functions?
[article]

2013
*
arXiv
*
pre-print

*In*this paper we study

*the*case

*of*

*approximate*degree and bounded-error quantum

*query*

*complexity*. ... It has long been known that any

*Boolean*

*function*that depends on

*n*input variables has both degree and exact quantum

*query*

*complexity*

*of*Omega(log

*n*), and that this bound is achieved for some

*functions*... Eq. (3) was observed

*in*email discussion between RdW and Scott Aaronson

*in*2008. We thank Artūrs Bačkurs, Oded Regev, Mario Szegedy, and

*the*anonymous CCC referees for useful comments and references. ...

##
###
Query Complexity Lower Bounds for Reconstruction of Codes

2014
*
Theory of Computing
*

We investigate

doi:10.4086/toc.2014.v010a019
dblp:journals/toc/ChakrabortyFM14
fatcat:pywkce2wbzcafhiraoogtyrzuy
*the*problem*of*local reconstruction, as defined by Saks and Seshadhri (2008) ,*in**the*context*of*error correcting codes. ...*The*first problem we address is that*of*message reconstruction, where given oracle access to a corrupted encoding w ∈ {0, 1}*n**of*some message x ∈ {0, 1} k our goal is to probabilistically recover x (or ... Seshadhri, David Garcia-Soreano and Ronald de Wolf for useful discussions on*the*topic.*In*particular, we thank Ronald de Wolf for many valuable comments on an early draft*of*this paper. ...##
###
Quantum Query-To-Communication Simulation Needs a Logarithmic Overhead

2020
*
Computational Complexity Conference
*

f) log

doi:10.4230/lipics.ccc.2020.32
dblp:conf/coco/0001CMP20
fatcat:e723bbz2bjcg7i5tl25ohqnxhe
*n*), where Q(f) is*the*bounded-error quantum*query**complexity**of*f. ... Buhrman, Cleve and Wigderson (STOC'98) observed that for every*Boolean**function*f:{-1,1}*ⁿ*→ {-1,1} and •:{-1,1}² → {-1,1}*the*two-party bounded-error quantum communication*complexity**of*(f ∘ •) is*O*(Q( ...*In*particular, we thank one*of**the*reviewers for pointing out*the*contrasts between*the*classical*query*model and*the*quantum*query*model that our results imply (Remark 5). ...##
###
Towards a Unifying Framework for Complex Query Processing over Structured Peer-to-Peer Data Networks
[chapter]

2004
*
Lecture Notes in Computer Science
*

Each peer stores routing information about

doi:10.1007/978-3-540-24629-9_13
fatcat:zichaif3lzfsrirnehgyrkg4di
*O*(d) other peers, which is independent*of**the*number*of*peers,*N*,*in**the*system. ...*In*this work we study how to process*complex**queries**in*DHT-based Peer-to-Peer (P2P) data networks.*Queries*are made over tuples and relations and are expressed*in*a*query*language, such as SQL. ... This means that,*in*case l=*O*(log(*N*), or l =*O*(*N*) we would have similar performance improvements for*the*processing*of*joins to those discussed for*the*processing*of*range*queries*. ...##
###
The Impact of Negation on the Complexity of the Shapley Value in Conjunctive Queries
[article]

2019
*
arXiv
*
pre-print

*In*this work, we investigate

*the*implication

*of*negation on

*the*

*complexity*

*of*Shapley computation,

*in*both

*the*exact and

*approximate*senses. ...

*In*particular, we have a thorough understanding

*of*

*the*tractability frontier for

*the*class

*of*Conjunctive

*Queries*(CQs) and aggregate

*functions*over CQs. ... [20] ,

*query*answering is viewed as a cooperative game where

*the*players are

*the*database facts and

*the*utility

*function*is

*the*

*query*answer,

*in*

*the*case

*of*aggregate

*queries*, or 0/1

*in*

*the*case

*of*

*Boolean*...

##
###
An Indexing and Retrieval Mechanism for Complex Similarity Queries in Image Databases

1999
*
Journal of Visual Communication and Image Representation
*

We also propose a new evaluation strategy to process

doi:10.1006/jvci.1999.0410
fatcat:kg4p74nuxvg7diezg5jynizns4
*the**complex*similarity*queries*. ...*The*proposed indexing scheme combines and extends*the*HG-tree,*the*signature file and*the*hashing scheme to support*complex*similarity*queries*. ... Since*the**complex*similarity*query*covers all other types*of**queries*, we will focus our attention on*the**complex*similarity*query**in*Section 4. ...
We concretely give a theoretical explanation that

doi:10.1145/2736277.2741628
dblp:conf/www/ShirakawaHN15
fatcat:edncawauwzdhxelbkyxzyw6pie
*the*IDF*of*a term is equal to*the*distance between*the*term and*the*empty string*in**the*space*of*information distance*in*which*the*Kolmogorov*complexity*...*The*results exemplified*the*potential*of**N*-gram IDF. ...*The*time*complexities*are*O*(df (g)·log |D|) for*N*-gram g and*O*(*N*· df (θ(g)) · log |D|) for θ(g),*the*conjunction*of*words composing g. ...
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