2011 IEEE 52nd Annual Symposium on Foundations of Computer Science最新文献

{"title":"Mechanism Design with Set-Theoretic Beliefs","authors":"Jiehua Chen, S. Micali","doi":"10.1109/FOCS.2011.11","DOIUrl":"https://doi.org/10.1109/FOCS.2011.11","url":null,"abstract":"In settings of incomplete information, we put forward (1) a very conservative -- indeed, purely set-theoretic -- model of the beliefs (including totally wrong ones) that each player may have about the payoff types of his opponents, and (2) a new and robust solution concept, based on mutual belief of rationality, capable of leveraging such conservative beliefs. We exemplify the applicability of our new approach for single-good auctions, by showing that, under our solution concept, a normal-form, simple, and deterministic mechanism guarantees -- up to an arbitrarily small, additive constant -- a revenue benchmark that is always greater than or equal to the second-highest valuation, and sometimes much greater. By contrast, we also prove that the same benchmark cannot even be approximated within any positive factor, under classical solution concepts.","PeriodicalId":326048,"journal":{"name":"2011 IEEE 52nd Annual Symposium on Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124563378","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}

{"title":"Near Linear Lower Bound for Dimension Reduction in L1","authors":"Alexandr Andoni, M. Charikar, Ofer Neiman, Huy L. Nguyen","doi":"10.1109/FOCS.2011.87","DOIUrl":"https://doi.org/10.1109/FOCS.2011.87","url":null,"abstract":"Given a set of $n$ points in $ell_{1}$, how many dimensions are needed to represent all pair wise distances within a specific distortion? This dimension-distortion tradeoff question is well understood for the $ell_{2}$ norm, where $O((log n)/epsilon^{2})$ dimensions suffice to achieve $1+epsilon$ distortion. In sharp contrast, there is a significant gap between upper and lower bounds for dimension reduction in $ell_{1}$. A recent result shows that distortion $1+epsilon$ can be achieved with $n/epsilon^{2}$ dimensions. On the other hand, the only lower bounds known are that distortion $delta$ requires $n^{Omega(1/delta^2)}$ dimensions and that distortion $1+epsilon$ requires $n^{1/2-O(epsilon log(1/epsilon))}$ dimensions. In this work, we show the first near linear lower bounds for dimension reduction in $ell_{1}$. In particular, we show that $1+epsilon$ distortion requires at least $n^{1-O(1/log(1/epsilon))}$ dimensions. Our proofs are combinatorial, but inspired by linear programming. In fact, our techniques lead to a simple combinatorial argument that is equivalent to the LP based proof of Brinkman-Charikar for lower bounds on dimension reduction in $ell_{1}$.","PeriodicalId":326048,"journal":{"name":"2011 IEEE 52nd Annual Symposium on Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127983891","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}

{"title":"New Extension of the Weil Bound for Character Sums with Applications to Coding","authors":"T. Kaufman, Shachar Lovett","doi":"10.1109/FOCS.2011.41","DOIUrl":"https://doi.org/10.1109/FOCS.2011.41","url":null,"abstract":"The Weil bound for character sums is a deep result in Algebraic Geometry with many applications both in mathematics and in the theoretical computer science. The Weil bound states that for any polynomial $f(x)$ over a finite field $mathbb{F}$ and any additive character $chi:mathbb{F} to mathbb{C}$, either $chi(f(x))$ is a constant function or it is distributed close to uniform. The Weil bound is quite effective as long as $deg(f) ll sqrt{|mathbb{F}|}$, but it breaks down when the degree of $f$ exceeds $sqrt{|mathbb{F}|}$. As the Weil bound plays a central role in many areas, finding extensions for polynomials of larger degree is an important problem with many possible applications. In this work we develop such an extension over finite fields $mathbb{F}_{p^n}$ of small characteristic: we prove that if $f(x)=g(x)+h(x)$ where $deg(g) ll sqrt{|mathbb{F}|}$ and $h(x)$ is a sparse polynomial of arbitrary degree but bounded weight degree, then the same conclusion of the classical Weil bound still holds: either $chi(f(x))$ is constant or its distribution is close to uniform. In particular, this shows that the sub code of Reed-Muller codes of degree $omega(1)$ generated by traces of sparse polynomials is a code with near optimal distance, while Reed-Muller of such a degree has no distance (i.e. $o(1)$ distance), this is one of the few examples where one can prove that sparse polynomials behave differently from non-sparse polynomials of the same degree. As an application we prove new general results for affine invariant codes. We prove that any affine-invariant subspace of quasi-polynomial size is (1) indeed a code (i.e. has good distance) and (2) is locally testable. Previous results for general affine invariant codes were known only for codes of polynomial size, and of length $2^n$ where $n$ needed to be a prime. Thus, our techniques are the first to extend to general families of such codes of super-polynomial size, where we also remove the requirement from $n$ to be a prime. The proof is based on two main ingredients: the extension of the Weil bound for character sums, and a new Fourier-analytic approach for estimating the weight distribution of general codes with large dual distance, which may be of independent interest.","PeriodicalId":326048,"journal":{"name":"2011 IEEE 52nd Annual Symposium on Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130212292","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}

{"title":"The Graph Minor Algorithm with Parity Conditions","authors":"K. Kawarabayashi, B. Reed, Paul Wollan","doi":"10.1109/FOCS.2011.52","DOIUrl":"https://doi.org/10.1109/FOCS.2011.52","url":null,"abstract":"We generalize the seminal Graph Minor algorithm of Robertson and Seymour to the parity version. We give polynomial time algorithms for the following problems:begin{enumerate}itemthe parity $H$-minor (Odd $K_k$-minor) containment problem, anditemthe disjoint paths problem with $k$ terminals and the parity condition for each path, end{enumerate}as well as several other related problems. We present an $O(m alpha(m,n) n)$ time algorithm for these problems for any fixed $k$, where $n,m$ are the number of vertices and the number of edges, respectively, and the function $alpha(m,n)$ is the inverse of the Ackermann function (see Tarjan cite{tarjan}). Note that the first problem includes the problem of testing whether or not a given graph contains $k$ disjoint odd cycles (which was recently solved in cite{tony, oddstoc}), if we fix $H$ to be equal to the graph of $k$ disjoint triangles. The algorithm for the second problem generalizes the Robertson Seymour algorithm for the $k$-disjoint paths problem. As with the Robertson-Seymour algorithm for the $k$-disjoint paths problem for any fixed $k$, in each iteration, we would like to either use the presence of a huge clique minor, or alternatively exploit the structure of graphs in which we cannot find such a minor. Here, however, we must maintain the parity of the paths and can only use an ``odd clique minor & quot;. This requires new techniques to describe the structure of the graph when we cannot find such a minor. We emphasize that our proof for the correctness of the above algorithms does not depend on the full power of the Graph Minor structure theorem cite{RS16}. Although the original Graph Minor algorithm of Robertson and Seymour does depend on it and our proof does have similarities to their arguments, we can avoid the structure theorem by building on the shorter proof for the correctness of the graph minor algorithm in cite{kw}. Consequently, we are able to avoid the much of the heavy machinery of the Graph Minor structure theory. Utilizing some results of cite{kw} and cite{lex1, lex2}, our proof is less than 50 pages.","PeriodicalId":326048,"journal":{"name":"2011 IEEE 52nd Annual Symposium on Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133623817","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}

{"title":"Storing Secrets on Continually Leaky Devices","authors":"Y. Dodis, Allison Bishop, Brent Waters, D. Wichs","doi":"10.1109/FOCS.2011.35","DOIUrl":"https://doi.org/10.1109/FOCS.2011.35","url":null,"abstract":"We consider the question of how to store a value secretly on devices that continually leak information about their internal state to an external attacker. If the secret value is stored on a single device from which it is efficiently retrievable, and the attacker can leak even a single predicate of the internal state of that device, then she may learn some information about the secret value itself. Therefore, we consider a setting where the secret value is shared between multiple devices (or multiple components of a single device), each of which continually leaks arbitrary adaptively chosen predicates its individual state. Since leakage is continual, each device must also continually update its state so that an attacker cannot just leak it entirely one bit at a time. In our model, the devices update their state individually and asynchronously, without any communication between them. The update process is necessarily randomized, and its randomness can leak as well. As our main result, we construct a sharing scheme for two devices, where a constant fraction of the internal state of each device can leak in between and during updates. Our scheme has the structure of a public-key encryption, where one share is a secret key and the other is a ciphertext. As a contribution of independent interest, we also get public-key encryption in the continual leakage model, introduced by Brakerski et al. and Dodis et al. (FOCS '10). This scheme tolerates continual leakage on the secret key and the updates, and simplifies the recent construction of Lewko, Lewko and Waters (STOC '11). For our main result, we show how to update the ciphertexts of the encryption scheme so that the message remains hidden even if an attacker interleaves leakage on secret key and ciphertext shares. The security of our scheme is based on the linear assumption in prime-order bilinear groups. We also provide an extension to general access structures realizable by linear secret sharing schemes across many devices. The main advantage of this extension is that the state of some devices can be compromised entirely, while that of the all remaining devices is susceptible to continual leakage. Lastly, we show impossibility of information theoretic sharing schemes in our model, where continually leaky devices update their state individually.","PeriodicalId":326048,"journal":{"name":"2011 IEEE 52nd Annual Symposium on Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124977584","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}

{"title":"Balls and Bins: Smaller Hash Families and Faster Evaluation","authors":"L. Elisa Celis, Omer Reingold, G. Segev, Udi Wieder","doi":"10.1137/120871626","DOIUrl":"https://doi.org/10.1137/120871626","url":null,"abstract":"A fundamental fact in the analysis of randomized algorithms is that when n balls are hashed into n bins independently and uniformly at random, with high probability each bin contains at most O(log n / log(log n)) balls. In various applications, however, the assumption that a truly random hash function is available is not always valid, and explicit functions are required. In this paper we study the size of families (or, equivalently, the description length of their functions) that guarantee a maximal load of O(log n / log(log n)) with high probability, as well as the evaluation time of their functions. Whereas such functions must be described using Omega(log n) bits, the best upper bound was formerly O(log^2 n / log(log n)) bits, which is attained by O(log n / log(log n))-wise independent functions. Traditional constructions of the latter offer an evaluation time of O(log n / log(log n)), which according to Siegel's lower bound [FOCS '89] can be reduced only at the cost of significantly increasing the description length. We construct two families that guarantee a maximal load of O(log n / log(log n)) with high probability. Our constructions are based on two different approaches, and exhibit different trade-offs between the description length and the evaluation time. The first construction shows that O(log n / log(log n))-wise independence can in fact be replaced by & quot; gradually increasing independence & quot;, resulting in functions that are described using O(log n log(log n)) bits and evaluated in time O(log n log(log n)). The second construction is based on derandomization techniques for space-bounded computations combined with a tailored construction of a pseudorandom generator, resulting in functions that are described using O(log^(3/2) n) bits and evaluated in time O(sqrt(log n)). The latter can be compared to Siegel's lower bound stating that O(log n / log(log n))-wise independent functions that are evaluated in time O(sqrt(log n)) must be described using Omega(2^(sqrt(log n))) bits.","PeriodicalId":326048,"journal":{"name":"2011 IEEE 52nd Annual Symposium on Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129680023","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}

{"title":"The Promise of Differential Privacy: A Tutorial on Algorithmic Techniques","authors":"C. Dwork","doi":"10.1109/FOCS.2011.88","DOIUrl":"https://doi.org/10.1109/FOCS.2011.88","url":null,"abstract":"{em Differential privacy} describes a promise, made by a data curator to a data subject: you will not be affected, adversely or otherwise, by allowing your data to be used in any study, no matter what other studies, data sets, or information from other sources is available. At their best, differentially private database mechanisms can make confidential data widely available for accurate data analysis, without resorting to data clean rooms, institutional review boards, data usage agreements, restricted views, or data protection plans. To enjoy the fruits of the research described in this tutorial, the data analyst must accept that raw data can never be accessed directly and that eventually data utility is consumed: overly accurate answers to too many questions will destroy privacy. The goal of algorithmic research on differential privacy is to postpone this inevitability as long as possible.","PeriodicalId":326048,"journal":{"name":"2011 IEEE 52nd Annual Symposium on Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127834429","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}

{"title":"Medium Access Using Queues","authors":"Devavrat Shah, Jinwoo Shin, P. Tetali","doi":"10.1109/FOCS.2011.99","DOIUrl":"https://doi.org/10.1109/FOCS.2011.99","url":null,"abstract":"Consider a wireless network of n nodes represented by a (undirected) graph G where an edge (i,j) models the fact that transmissions of i and j interfere with each other, i.e. simultaneous transmissions of i and j become unsuccessful. Hence it is required that at each time instance a set of non-interfering nodes (corresponding to an independent set in G) access the wireless medium. To utilize wireless resources efficiently, it is required to arbitrate the access of medium among interfering nodes properly. Moreover, to be of practical use, such a mechanism is required to be totally distributed as well as simple. As the main result of this paper, we provide such a medium access algorithm. It is randomized, totally distributed and simple: each node attempts to access medium at each time with probability that is a function of its local information. We establish efficiency of the algorithm by showing that the corresponding network Markov chain is positive recurrent as long as the demand imposed on the network can be supported by the wireless network (using any algorithm). In that sense, the proposed algorithm is optimal in terms of utilizing wireless resources. The algorithm is oblivious to the network graph structure, in contrast with the so-called polynomial back-off algorithm by Hastad-Leighton-Rogoff (STOC '87, SICOMP '96) that is established to be optimal for the complete graph and bipartite graphs (by Goldberg-MacKenzie (SODA '96, JCSS '99)).","PeriodicalId":326048,"journal":{"name":"2011 IEEE 52nd Annual Symposium on Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128746699","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}

{"title":"An FPTAS for #Knapsack and Related Counting Problems","authors":"Parikshit Gopalan, Adam R. Klivans, R. Meka, Daniel Stefankovic, S. Vempala, Eric Vigoda","doi":"10.1109/FOCS.2011.32","DOIUrl":"https://doi.org/10.1109/FOCS.2011.32","url":null,"abstract":"Given $n$ elements with non-negative integer weights $w_1,..., w_n$ and an integer capacity $C$, we consider the counting version of the classic knapsack problem: find the number of distinct subsets whose weights add up to at most $C$. We give the first deterministic, fully polynomial-time approximation scheme (FPTAS) for estimating the number of solutions to any knapsack constraint (our estimate has relative error $1 pm epsilon$). Our algorithm is based on dynamic programming. Previously, randomized polynomial-time approximation schemes (FPRAS) were known first by Morris and Sinclair via Markov chain Monte Carlo techniques, and subsequently by Dyer via dynamic programming and rejection sampling. In addition, we present a new method for deterministic approximate counting using {em read-once branching programs.} Our approach yields an FPTAS for several other counting problems, including counting solutions for the multidimensional knapsack problem with a constant number of constraints, the general integer knapsack problem, and the contingency tables problem with a constant number of rows.","PeriodicalId":326048,"journal":{"name":"2011 IEEE 52nd Annual Symposium on Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123456756","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}

{"title":"Evolution with Recombination","authors":"Varun Kanade","doi":"10.1109/FOCS.2011.24","DOIUrl":"https://doi.org/10.1109/FOCS.2011.24","url":null,"abstract":"Valiant (2007) introduced a computational model of evolution and suggested that Darwinian evolution be studied in the framework of computational learning theory. Valiant describes evolution as a restricted form of learning where exploration is limited to a set of possible mutations and feedback is received through the survival of the fittest mutation. In subsequent work Feldman (2008) showed that evolvability in Valiant's model is equivalent to learning in the correlational statistical query (CSQ) model. We extend Valiant's model to include genetic recombination and show that in certain cases, recombination can significantly speed-up the process of evolution in terms of the number of generations, though at the expense of population size. This follows via a reduction from parallel-CSQ algorithms to evolution with recombination. This gives an exponential speed-up (in terms of the number of generations) over previous known results for evolving conjunctions and half spaces with respect to restricted distributions.","PeriodicalId":326048,"journal":{"name":"2011 IEEE 52nd Annual Symposium on Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123621836","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}