Proceedings of the forty-sixth annual ACM symposium on Theory of computing最新文献

{"title":"How to use indistinguishability obfuscation: deniable encryption, and more","authors":"A. Sahai, Brent Waters","doi":"10.1145/2591796.2591825","DOIUrl":"https://doi.org/10.1145/2591796.2591825","url":null,"abstract":"We introduce a new technique, that we call punctured programs, to apply indistinguishability obfuscation towards cryptographic problems. We use this technique to carry out a systematic study of the applicability of indistinguishability obfuscation to a variety of cryptographic goals. Along the way, we resolve the 16-year-old open question of Deniable Encryption, posed by Canetti, Dwork, Naor, and Ostrovsky in 1997: In deniable encryption, a sender who is forced to reveal to an adversary both her message and the randomness she used for encrypting it should be able to convincingly provide \"fake\" randomness that can explain any alternative message that she would like to pretend that she sent. We resolve this question by giving the first construction of deniable encryption that does not require any pre-planning by the party that must later issue a denial. In addition, we show the generality of our punctured programs technique by also constructing a variety of core cryptographic objects from indistinguishability obfuscation and one-way functions (or close variants). In particular we obtain: public key encryption, short \"hash-and-sign\" selectively secure signatures, chosen-ciphertext secure public key encryption, non-interactive zero knowledge proofs (NIZKs), injective trapdoor functions, and oblivious transfer. These results suggest the possibility of indistinguishability obfuscation becoming a \"central hub\" for cryptography.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133895392","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 power of localization for efficiently learning linear separators with noise","authors":"Pranjal Awasthi, Maria-Florina Balcan, Philip M. Long","doi":"10.1145/2591796.2591839","DOIUrl":"https://doi.org/10.1145/2591796.2591839","url":null,"abstract":"We introduce a new approach for designing computationally efficient and noise tolerant algorithms for learning linear separators. We consider the malicious noise model of Valiant [41, 32] and the adversarial label noise model of Kearns, Schapire, and Sellie [34]. For malicious noise, where the adversary can corrupt an η of fraction both the label part and the feature part, we provide a polynomial-time algorithm for learning linear separators in Rd under the uniform distribution with nearly information-theoretically optimal noise tolerance of η = Ω(ε), improving on the Ω(&epsilon/d1/4) noise-tolerance of [31] and the Ω(ε2/log(d/ε) of [35]. For the adversarial label noise model, where the distribution over the feature vectors is unchanged, and the overall probability of a noisy label is constrained to be at most η, we give a polynomial-time algorithm for learning linear separators in Rd under the uniform distribution that can also handle a noise rate of η = Ω(ε). This improves over the results of [31] which either required runtime super-exponential in 1/ε (ours is polynomial in 1/ε) or tolerated less noise. In the case that the distribution is isotropic log-concave, we present a polynomial-time algorithm for the malicious noise model that tolerates Ω(ε/log2(1/ε)) noise, and a polynomial-time algorithm for the adversarial label noise model that also handles Ω(ε/log2(1/ε)) noise. Both of these also improve on results from [35]. In particular, in the case of malicious noise, unlike previous results, our noise tolerance has no dependence on the dimension d of the space. Our algorithms are also efficient in the active learning setting, where learning algorithms only receive the classifications of examples when they ask for them. We show that, in this model, our algorithms achieve a label complexity whose dependence on the error parameter ε is polylogarithmic (and thus exponentially better than that of any passive algorithm). This provides the first polynomial time active learning algorithm for learning linear separators in the presence of malicious noise or adversarial label noise.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"215 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114745917","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":"A super-polynomial lower bound for regular arithmetic formulas","authors":"N. Kayal, Chandan Saha, Ramprasad Saptharishi","doi":"10.1145/2591796.2591847","DOIUrl":"https://doi.org/10.1145/2591796.2591847","url":null,"abstract":"We consider arithmetic formulas consisting of alternating layers of addition (+) and multiplication (×) gates such that the fanin of all the gates in any fixed layer is the same. Such a formula Φ which additionally has the property that its formal/syntactic degree is at most twice the (total) degree of its output polynomial, we refer to as a regular formula. As usual, we allow arbitrary constants from the underlying field F on the incoming edges to a + gate so that a + gate can in fact compute an arbitrary F-linear combination of its inputs. We show that there is an (n2 + 1)-variate polynomial of degree 2n in VNP such that any regular formula computing it must be of size at least nΩ(log n). Along the way, we examine depth four (ΣΠΣΠ) regular formulas wherein all multiplication gates in the layer adjacent to the inputs have fanin a and all multiplication gates in the layer adjacent to the output node have fanin b. We refer to such formulas as ΣΠ[b]ΣΠ[a]-formulas. We show that there exists an n2-variate polynomial of degree n in VNP such that any ΣΠ[O(√n)]ΣΠ[√n]-formula computing it must have top fan-in at least 2Ω(√n·log n). In comparison, Tavenas [Tav13] has recently shown that every nO(1)-variate polynomial of degree n in VP admits a ΣΠ[O(√n)]ΣΠ[√n]-formula of top fan-in 2O(√n·log n). This means that any further asymptotic improvement in our lower bound for such formulas (to say 2ω(√n log n)) will imply that VP is different from VNP.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132318467","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 almost-optimally fair three-party coin-flipping protocol","authors":"Iftach Haitner, Eliad Tsfadia","doi":"10.1145/2591796.2591842","DOIUrl":"https://doi.org/10.1145/2591796.2591842","url":null,"abstract":"In a multiparty fair coin-flipping protocol, the parties output a common (close to) unbiased bit, even when some corrupted parties try to bias the output. Cleve [STOC 1986] has shown that in the case of dishonest majority (i.e., at least half of the parties can be corrupted), in any m-round coin-flipping protocol, the corrupted parties can bias the honest parties' common output bit by Ω(1/m). For more than two decades, the best known coin-flipping protocols against dishonest majority had bias [EQUATION], where ℓ is the number of corrupted parties. This was changed by a recent breakthrough result of Moran et al. [TCC 2009], who constructed an m-round, two-party coin-flipping protocol with optimal bias Θ(1/m). In a subsequent work, Beimel et al. [Crypto 2010] extended this result to the multiparty case in which less than 2/3 of the parties can be corrupted. Still for the case of 2/3 (or more) corrupted parties, the best known protocol had bias [EQUATION]. In particular, this was the state of affairs for the natural three-party case. We make a step towards eliminating the above gap, presenting an m-round, three-party coin-flipping protocol, with bias O(log2m)/m. Our approach (which we also apply for the two-party case) does not follow the \"threshold round\" paradigm used in the work of Moran et al. and Beimel et al., but rather is a variation of the majority protocol of Cleve, used to obtain the aforementioned [EQUATION]-bias protocol.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129472437","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":"Optimal CUR matrix decompositions","authors":"Christos Boutsidis, David P. Woodruff","doi":"10.1145/2591796.2591819","DOIUrl":"https://doi.org/10.1145/2591796.2591819","url":null,"abstract":"The CUR decomposition of an m×n matrix A finds an m×c matrix C with a small subset of c < n columns of A, together with an r×n matrix R with a small subset of r < m rows of A, as well as a c×r low rank matrix U such that the matrix CUR approximates the input matrix A, that is, ||A --- CUR||2F ≤ (1 + ε)||A --- Ak||2F, where ||.||F denotes the Frobenius norm, 0 < ε < 1 is an accuracy parameter, and Ak is the best m × n matrix of rank k constructed via the SVD of A. We present input-sparsity-time and deterministic algorithms for constructing such a CUR matrix decomposition of A where c = O(k/ε) and r = O(k/ε) and rank(U) = k. Up to constant factors, our construction is simultaneously optimal in c, r, and rank(U).","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128241271","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":"Competitive algorithms from competitive equilibria: non-clairvoyant scheduling under polyhedral constraints","authors":"Sungjin Im, Janardhan Kulkarni, Kamesh Munagala","doi":"10.1145/2591796.2591814","DOIUrl":"https://doi.org/10.1145/2591796.2591814","url":null,"abstract":"We introduce and study a general scheduling problem that we term the Packing Scheduling problem (PSP). In this problem, jobs can have different arrival times and sizes; a scheduler can process job j at rate xj, subject to arbitrary packing constraints over the set of rates (x) of the outstanding jobs. The PSP framework captures a variety of scheduling problems, including the classical problems of unrelated machines scheduling, broadcast scheduling, and scheduling jobs of different parallelizability. It also captures scheduling constraints arising in diverse modern environments ranging from individual computer architectures to data centers. More concretely, PSP models multidimensional resource requirements and parallelizability, as well as network bandwidth requirements found in data center scheduling. In this paper, we design non-clairvoyant online algorithms for PSP and its special cases -- in this setting, the scheduler is unaware of the sizes of jobs. Our results are summarized as follows. • For minimizing total weighted completion time, we show a O(1)-competitive algorithm. Surprisingly, we achieve this result by applying the well-known Proportional Fairness algorithm (PF) to perform allocations each time instant. Though PF has been extensively studied in the context of maximizing fairness in resource allocation, we present the first analysis in adversarial and general settings for optimizing job latency. Our result is also the first O(1)-competitive algorithm for weighted completion time for several classical non-clairvoyant scheduling problems. •For minimizing total weighted flow time, for any constant ε > 0, any O(n1---ε)-competitive algorithm requires extra speed (resource augmentation) compared to the offline optimum. We show that PF is a O(log n)-speed O(log n)-competitive non-clairvoyant algorithm, where n is the total number of jobs. We further show that there is an instance of PSP for which no non-clairvoyant algorithm can be O(n1---ε)-competitive with o(√log n) speed. •For the classical problem of minimizing total flow time for unrelated machines in the non-clairvoyant setting, we present the first online algorithm which is scalable ((1 + ε)-speed O(1)-competitive for any constant ε > 0). No non-trivial results were known for this setting, and the previous scalable algorithm could handle only related machines. We develop new algorithmic techniques to handle the unrelated machines setting that build on a new single machine scheduling policy. Since unrelated machine scheduling is a special case of PSP, when contrasted with the lower bound for PSP, our result also shows that PSP is significantly harder than perhaps the most general classical scheduling settings. Our results for PSP show that instantaneous fair scheduling algorithms can also be effective tools for minimizing the overall job latency, even when the scheduling decisions are non-clairvoyant and constrained by general packing constraints.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121251544","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":"Cluster before you hallucinate: approximating node-capacitated network design and energy efficient routing","authors":"Ravishankar Krishnaswamy, V. Nagarajan, K. Pruhs, Cliff Stein","doi":"10.1145/2591796.2591831","DOIUrl":"https://doi.org/10.1145/2591796.2591831","url":null,"abstract":"We consider circuit routing with an objective of minimizing energy, in a network of routers that are speed scalable and that may be shutdown when idle. It is known that this energy minimization problem can be reduced to a capacitated flow network design problem, where vertices have a common capacity but arbitrary costs, and the goal is to choose a minimum cost collection of vertices whose induced subgraph will support the specified flow requirements. For the multicast (single-sink) capacitated design problem we give a polynomial-time algorithm that is O(log3 n)- approximate with O(log4 n) congestion. This translates back to a O(log4α+3 n)-approximation for the multicast energy-minimization routing problem, where α is the polynomial exponent in the dynamic power used by a router. For the unicast (multicommodity) capacitated design problem we give a polynomial-time algorithm that is O(log5 n)-approximate with O(log12 n) congestion, which translates back to a O(log12α+5 n)-approximation for the unicast energy-minimization routing problem.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127738316","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":"Distributed approximation algorithms for weighted shortest paths","authors":"Danupon Nanongkai","doi":"10.1145/2591796.2591850","DOIUrl":"https://doi.org/10.1145/2591796.2591850","url":null,"abstract":"A distributed network is modeled by a graph having n nodes (processors) and diameter D. We study the time complexity of approximating weighted (undirected) shortest paths on distributed networks with a O (log n) bandwidth restriction on edges (the standard synchronous CONGEST model). The question whether approximation algorithms help speed up the shortest paths and distance computation (more precisely distance computation) was raised since at least 2004 by Elkin (SIGACT News 2004). The unweighted case of this problem is well-understood while its weighted counterpart is fundamental problem in the area of distributed approximation algorithms and remains widely open. We present new algorithms for computing both single-source shortest paths (SSSP) and all-pairs shortest paths (APSP) in the weighted case. Our main result is an algorithm for SSSP. Previous results are the classic O(n)-time Bellman-Ford algorithm and an Õ(n1/2+1/2k + D)-time (8k⌈log(k + 1)⌉ --1)-approximation algorithm, for any integer k ≥ 1, which follows from the result of Lenzen and Patt-Shamir (STOC 2013). (Note that Lenzen and Patt-Shamir in fact solve a harder problem, and we use Õ(·) to hide the O(poly log n) term.) We present an Õ (n1/2D1/4 + D)-time (1 + o(1))-approximation algorithm for SSSP. This algorithm is sublinear-time as long as D is sublinear, thus yielding a sublinear-time algorithm with almost optimal solution. When D is small, our running time matches the lower bound of Ω(n1/2 + D) by Das Sarma et al. (SICOMP 2012), which holds even when D=Θ(log n), up to a poly log n factor. As a by-product of our technique, we obtain a simple Õ (n)-time (1+ o(1))-approximation algorithm for APSP, improving the previous Õ(n)-time O(1)-approximation algorithm following from the results of Lenzen and Patt-Shamir. We also prove a matching lower bound. Our techniques also yield an Õ(n1/2) time algorithm on fully-connected networks, which guarantees an exact solution for SSSP and a (2+ o(1))-approximate solution for APSP. All our algorithms rely on two new simple tools: light-weight algorithm for bounded-hop SSSP and shortest-path diameter reduction via shortcuts. These tools might be of an independent interest and useful in designing other distributed algorithms.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126951336","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":"Online local learning via semidefinite programming","authors":"Paul Christiano","doi":"10.1145/2591796.2591880","DOIUrl":"https://doi.org/10.1145/2591796.2591880","url":null,"abstract":"In many online learning problems we are interested in predicting local information about some universe of items. For example, we may want to know whether two items are in the same cluster rather than computing an assignment of items to clusters; we may want to know which of two teams will win a game rather than computing a ranking of teams. Although finding the optimal clustering or ranking is typically intractable, it may be possible to predict the relationships between items as well as if you could solve the global optimization problem exactly. Formally, we consider an online learning problem in which a learner repeatedly guesses a pair of labels (ℓ(x), ℓ(y)) and receives an adversarial payoff depending on those labels. The learner's goal is to receive a payoff as good as the best fixed labeling of the items. We show that a simple algorithm based on semidefinite programming can achieve asymptotically optimal regret in the case where the number of possible labels is constant, resolving an open problem posed by Hazan, Kale, and Shalev-Schwartz [10]. Our main technical contribution is a novel use and analysis of the log det regularizer, exploiting the observation that log det (Σ + I) upper bounds the entropy of any distribution with covariance matrix Σ.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130718160","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":"Zig-zag sort: a simple deterministic data-oblivious sorting algorithm running in O(n log n) time","authors":"M. Goodrich","doi":"10.1145/2591796.2591830","DOIUrl":"https://doi.org/10.1145/2591796.2591830","url":null,"abstract":"We describe Zig-zag Sort---a deterministic data-oblivious sorting algorithm running in O(n log n) time that is arguably simpler than previously known algorithms with similar properties, which are based on the AKS sorting network. Because it is data-oblivious and deterministic, Zig-zag Sort can be implemented as a simple O(n log n)-size sorting network, thereby providing a solution to an open problem posed by Incerpi and Sedgewick in 1985. In addition, Zig-zag Sort is a variant of Shellsort, and is, in fact, the first deterministic Shellsort variant running in O(n log n) time. The existence of such an algorithm was posed as an open problem by Plaxton et al. in 1992 and also by Sedgewick in 1996. More relevant for today is the fact that the existence of a simple data-oblivious deterministic sorting algorithm running in O(n log n) time simplifies the \"inner-loop\" computation in several proposed oblivious-RAM simulation methods (which utilize AKS sorting networks), and this, in turn, implies simplified mechanisms for privacy-preserving data outsourcing in several cloud computing applications.","PeriodicalId":123501,"journal":{"name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","volume":"246 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115562460","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}