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

Dana Ron, Ronitt Rubinfeld, Muli Safra, Omri Weinstein
2011 arXiv   pre-print
We study 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.  ... 
arXiv:1101.5345v1 fatcat:la5grhg2tbd4bk5cd5kwbhdvri

Approximating the Influence of Monotone Boolean Functions in O(√n) Query Complexity

Dana Ron, Ronitt Rubinfeld, Muli Safra, Alex Samorodnitsky, Omri Weinstein
2012 ACM Transactions on Computation Theory  
We study 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 On 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.  ... 
doi:10.1145/2382559.2382562 fatcat:qfookvmparhxtfrrg234jlhsf4

The Query Complexity of Certification [article]

Guy Blanc, Caleb Koch, Jane Lange, Li-Yang Tan
2022 arXiv   pre-print
Our main result is a new algorithm for certifying 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.  ... 
arXiv:2201.07736v2 fatcat:nt4dle3glnd23kvd5mmln7fhcu

Graphical Models: Queries, Complexity, Algorithms

Martin C. Cooper, Simon de Givry, Thomas Schiex, Markus Bläser, Christophe Paul
2020 Symposium on Theoretical Aspects of Computer Science  
Graphical models (GMs) define a family 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] .  ... 
doi:10.4230/lipics.stacs.2020.4 dblp:conf/stacs/CooperGS20 fatcat:rqyjypnqozd47frmaobbcpo5ei

Query Complexity of Derivative-Free Optimization [article]

Kevin G. Jamieson, Robert D. Nowak, Benjamin Recht
2012 arXiv   pre-print
A distinctive feature 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 nσ 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  ... 
arXiv:1209.2434v1 fatcat:ne47u4bjyneprdfnhljafdm6my

Efficient Inference for Complex Queries on Complex Distributions

Lili Dworkin, Michael J. Kearns, Lirong Xia
2014 International Conference on Artificial Intelligence and Statistics  
We consider problems 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.  ... 
dblp:conf/aistats/DworkinKX14 fatcat:l4asmhfobrcrngopofjklpe43i

How Low can Approximate Degree and Quantum Query Complexity be for Total Boolean Functions?

Andris Ambainis, Ronald de Wolf
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  ... 
doi:10.1007/s00037-014-0083-2 fatcat:cva7ccas5ncatnyrtyyatyvoca

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

Andris Ambainis, Ronald de Wolf
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  ... 
doi:10.1109/ccc.2013.26 dblp:conf/coco/AmbainisW13 fatcat:mfjmjs64s5ckxfjf5xeomgfnxu

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

Andris Ambainis and Ronald de Wolf (CWI and U of Amsterdam)
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.  ... 
arXiv:1206.0717v2 fatcat:65tbomget5gzpfcgqq7dqyhrfe

Query Complexity Lower Bounds for Reconstruction of Codes

Sourav Chakraborty, Eldar Fischer, Arie Matsliah
2014 Theory of Computing  
We investigate 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.  ... 
doi:10.4086/toc.2014.v010a019 dblp:journals/toc/ChakrabortyFM14 fatcat:pywkce2wbzcafhiraoogtyrzuy

Quantum Query-To-Communication Simulation Needs a Logarithmic Overhead

Sourav Chakraborty, Arkadev Chattopadhyay, Nikhil S. Mande, Manaswi Paraashar, Shubhangi Saraf
2020 Computational Complexity Conference  
f) log 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} → {-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).  ... 
doi:10.4230/lipics.ccc.2020.32 dblp:conf/coco/0001CMP20 fatcat:e723bbz2bjcg7i5tl25ohqnxhe

Towards a Unifying Framework for Complex Query Processing over Structured Peer-to-Peer Data Networks [chapter]

Peter Triantafillou, Theoni Pitoura
2004 Lecture Notes in Computer Science  
Each peer stores routing information about 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.  ... 
doi:10.1007/978-3-540-24629-9_13 fatcat:zichaif3lzfsrirnehgyrkg4di

The Impact of Negation on the Complexity of the Shapley Value in Conjunctive Queries [article]

Alon Reshef, Benny Kimelfeld, Ester Livshits
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  ... 
arXiv:1912.12610v1 fatcat:7gitrwf6znh5fl2oh2jhuuf2ty

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

Guang-Ho Cha, Chin-Wan Chung
1999 Journal of Visual Communication and Image Representation  
We also propose a new evaluation strategy to process 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.  ... 
doi:10.1006/jvci.1999.0410 fatcat:kg4p74nuxvg7diezg5jynizns4

N-gram IDF

Masumi Shirakawa, Takahiro Hara, Shojiro Nishio
2015 Proceedings of the 24th International Conference on World Wide Web - WWW '15  
We concretely give a theoretical explanation that 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.  ... 
doi:10.1145/2736277.2741628 dblp:conf/www/ShirakawaHN15 fatcat:edncawauwzdhxelbkyxzyw6pie
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