2010 IEEE 51st Annual Symposium on Foundations of Computer Science最新文献_第2页

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1137/100814998

Emanuele Viola

{"title":"The Complexity of Distributions","authors":"Emanuele Viola","doi":"10.1137/100814998","DOIUrl":"https://doi.org/10.1137/100814998","url":null,"abstract":"Complexity theory typically studies the complexity of computing a function $h(x) : zo^m to zo^n$ of a given input $x$. We advocate the study of the complexity of generating the distribution $h(x)$ for uniform $x$, given random bits. Our main results are: (1) Any function $f : zo^ell to zon$ such that (i) each output bit $f_i$ depends on $o(log n)$ input bits, and (ii) $ell le log_2 binom{n}{alpha n} + n^{0.99}$, has output distribution $f(U)$ at statistical distance $ge 1 - 1/n^{0.49}$ from the uniform distribution over $n$-bit strings of hamming weight $alpha n$. We also prove lower bounds for generating $(X,b(X))$ for boolean $b$, and in the case in which each bit $f_i$ is a small-depth decision tree. These lower bounds seem to be the first of their kind, the proofs use anti-concentration results for the sum of random variables. (2) Lower bounds for generating distributions imply succinct data structures lower bounds. As a corollary of (1), we obtain the first lower bound for the membership problem of representing a set $S subseteq [n]$ of size $alpha n$, in the case where $1/alpha$ is a power of $2$: If queries ``$i in S$?'' are answered by non-adaptively probing $o(log n)$ bits, then the representation uses $ge log_2 binom{n}{alpha n} + Omega(log n)$ bits. (3) Upper bounds complementing the bounds in (1) for various settings of parameters. (4) Uniform randomized $acz$ circuits of $poly(n)$ size and depth $d = O(1)$ with error $e$ can be simulated by uniform randomized $acz$ circuits of $poly(n)$ size and depth $d+1$ with error $e + o(1)$ using $le (log n)^{O( log log n)}$ random bits. Previous derandomizations [Ajtai and Wigderson '85, Nisan '91] increase the depth by a constant factor, or else have poor seed length.","PeriodicalId":228365,"journal":{"name":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117007385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 49

Agnostically Learning under Permutation Invariant Distributions 排列不变分布下的不可知论学习

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1109/FOCS.2010.17

K. Wimmer

{"title":"Agnostically Learning under Permutation Invariant Distributions","authors":"K. Wimmer","doi":"10.1109/FOCS.2010.17","DOIUrl":"https://doi.org/10.1109/FOCS.2010.17","url":null,"abstract":"We generalize algorithms from computational learning theory that are successful under the uniform distribution on the Boolean hypercube ${0,1}^n$ to algorithms successful on permutation invariant distributions. A permutation invariant distribution is a distribution where the probability mass remains constant upon permutations in the instances. While the tools in our generalization mimic those used for the Boolean hypercube, the fact that permutation invariant distributions are not product distributions presents a significant obstacle. Under the uniform distribution, half spaces can be agnostically learned in polynomial time for constant $eps$. The main tools used are a theorem of Peres~cite{Peres04} bounding the {it noise sensitivity} of a half space, a result of~cite{KOS04} that this theorem implies Fourier concentration, and a modification of the Low-Degree algorithm of Linial, Man sour, Nisan~cite{LMN:93} made by Kalai et. al.~cite{KKMS08}. These results are extended to arbitrary product distributions in~cite{BOWi08}. We prove analogous results for permutation invariant distributions, more generally, we work in the domain of the symmetric group. We define noise sensitivity in this setting, and show that noise sensitivity has a nice combinatorial interpretation in terms of Young tableaux. The main technical innovations involve techniques from the representation theory of the symmetric group, especially the combinatorics of Young tableaux. We show that low noise sensitivity implies concentration on “simple'' components of the Fourier spectrum, and that this fact will allow us to agnostically learn half spaces under permutation invariant distributions to constant accuracy in roughly the same time as in the uniform distribution over the Boolean hypercube case.","PeriodicalId":228365,"journal":{"name":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114879144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 11

Black-Box Randomized Reductions in Algorithmic Mechanism Design 算法机制设计中的黑盒随机约简

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1137/110843654

S. Dughmi, T. Roughgarden

引用次数: 67

Fighting Perebor: New and Improved Algorithms for Formula and QBF Satisfiability 对抗缺陷:公式和QBF可满足性的新改进算法

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1109/FOCS.2010.25

R. Santhanam

{"title":"Fighting Perebor: New and Improved Algorithms for Formula and QBF Satisfiability","authors":"R. Santhanam","doi":"10.1109/FOCS.2010.25","DOIUrl":"https://doi.org/10.1109/FOCS.2010.25","url":null,"abstract":"We investigate the possibility of finding satisfying assignments to Boolean formulae and testing validity of quantified Boolean formulae (QBF) asymptotically faster than a brute force search. Our first main result is a simple deterministic algorithm running in time $2^{n - Omega(n)}$ for satisfiability of formulae of linear size in $n$, where $n$ is the number of variables in the formula. This algorithm extends to exactly counting the number of satisfying assignments, within the same time bound. Our second main result is a deterministic algorithm running in time $2^{n - Omega(n/log(n))}$ for solving QBFs in which the number of occurrences of any variable is bounded by a constant. For instances which are ``structured'', in a certain precise sense, the algorithm can be modified to run in time $2^{n - Omega(n)}$. To the best of our knowledge, no non-trivial algorithms were known for these problems before. As a byproduct of the technique used to establish our first main result, we show that every function computable by linear-size formulae can be represented by decision trees of size $2^{n - Omega(n)}$. As a consequence, we get strong super linear {it average-case} formula size lower bounds for the Parity function.","PeriodicalId":228365,"journal":{"name":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126343448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 87

Overcoming the Hole in the Bucket: Public-Key Cryptography Resilient to Continual Memory Leakage 克服桶中的洞:对持续内存泄漏具有弹性的公钥加密

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1109/FOCS.2010.55

Zvika Brakerski, Y. Kalai, Jonathan Katz, V. Vaikuntanathan

引用次数: 219

Approximation Algorithms for the Edge-Disjoint Paths Problem via Raecke Decompositions 基于Raecke分解的边不相交路径问题逼近算法

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1109/FOCS.2010.33

M. Andrews

引用次数: 32

A Multiplicative Weights Mechanism for Privacy-Preserving Data Analysis 隐私保护数据分析的乘权机制

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1109/FOCS.2010.85

Moritz Hardt, G. Rothblum

{"title":"A Multiplicative Weights Mechanism for Privacy-Preserving Data Analysis","authors":"Moritz Hardt, G. Rothblum","doi":"10.1109/FOCS.2010.85","DOIUrl":"https://doi.org/10.1109/FOCS.2010.85","url":null,"abstract":"We consider statistical data analysis in the interactive setting. In this setting a trusted curator maintains a database of sensitive information about individual participants, and releases privacy-preserving answers to queries as they arrive. Our primary contribution is a new differentially private multiplicative weights mechanism for answering a large number of interactive counting (or linear) queries that arrive online and may be adaptively chosen. This is the first mechanism with worst-case accuracy guarantees that can answer large numbers of interactive queries and is {em efficient} (in terms of the runtime's dependence on the data universe size). The error is asymptotically emph{optimal} in its dependence on the number of participants, and depends only logarithmically on the number of queries being answered. The running time is nearly {em linear} in the size of the data universe. As a further contribution, when we relax the utility requirement and require accuracy only for databases drawn from a rich class of databases, we obtain exponential improvements in running time. Even in this relaxed setting we continue to guarantee privacy for {em any} input database. Only the utility requirement is relaxed. Specifically, we show that when the input database is drawn from a {em smooth} distribution — a distribution that does not place too much weight on any single data item — accuracy remains as above, and the running time becomes {em poly-logarithmic} in the data universe size. The main technical contributions are the application of multiplicative weights techniques to the differential privacy setting, a new privacy analysis for the interactive setting, and a technique for reducing data dimensionality for databases drawn from smooth distributions.","PeriodicalId":228365,"journal":{"name":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131696287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 411

On the Queue Number of Planar Graphs 关于平面图的队列数

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1109/FOCS.2010.42

G. Battista, Fabrizio Frati, J. Pach

引用次数: 49

All-Pairs Shortest Paths in O(n²) Time with High Probability O(n²)时间内高概率的全对最短路径

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1145/2508028.2505988

Y. Peres, D. Sotnikov, B. Sudakov, Uri Zwick

引用次数: 24

Logspace Versions of the Theorems of Bodlaender and Courcelle Bodlaender定理和Courcelle定理的对数空间版本

2010 IEEE 51st Annual Symposium on Foundations of Computer Science Pub Date : 2010-10-23 DOI: 10.1109/FOCS.2010.21

Michael Elberfeld, A. Jakoby, Till Tantau

引用次数: 131