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256
Smooth sensitivity and sampling in private data analysis
 In STOC
, 2007
"... We introduce a new, generic framework for private data analysis. The goal of private data analysis is to release aggregate information about a data set while protecting the privacy of the individuals whose information the data set contains. Our framework allows one to release functions f of the data ..."
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Cited by 168 (16 self)
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We introduce a new, generic framework for private data analysis. The goal of private data analysis is to release aggregate information about a data set while protecting the privacy of the individuals whose information the data set contains. Our framework allows one to release functions f of the data with instancebased additive noise. That is, the noise magnitude is determined not only by the function we want to release, but also by the database itself. One of the challenges is to ensure that the noise magnitude does not leak information about the database. To address that, we calibrate the noise magnitude to the smooth sensitivity of f on the database x — a measure of variability of f in the neighborhood of the instance x. The new framework greatly expands the applicability of output perturbation, a technique for protecting individuals ’ privacy by adding a small amount of random noise to the released statistics. To our knowledge, this is the first formal analysis of the effect of instancebased noise in the context of data privacy. Our framework raises many interesting algorithmic questions. Namely, to apply the framework one must compute or approximate the smooth sensitivity of f on x. We show how to do this efficiently for several different functions, including the median and the cost of the minimum spanning tree. We also give a generic procedure based on sampling that allows one to release f(x) accurately on many databases x. This procedure is applicable even when no efficient algorithm for approximating smooth sensitivity of f is known or when f is given as a black box. We illustrate the procedure by applying it to kSED (kmeans) clustering and learning mixtures of Gaussians.
Computing correlated equilibria in MultiPlayer Games
 STOC'05
, 2005
"... We develop a polynomialtime algorithm for finding correlated equilibria (a wellstudied notion of rationality due to Aumann that generalizes the Nash equilibrium) in a broad class of succinctly representable multiplayer games, encompassing essentially all known kinds, including all graphical games, ..."
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Cited by 95 (6 self)
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We develop a polynomialtime algorithm for finding correlated equilibria (a wellstudied notion of rationality due to Aumann that generalizes the Nash equilibrium) in a broad class of succinctly representable multiplayer games, encompassing essentially all known kinds, including all graphical games, polymatrix games, congestion games, scheduling games, local effect games, as well as several generalizations. Our algorithm is based on a variant of the existence proof due to Hart and Schmeidler [11], and employs linear programming duality, the ellipsoid algorithm, Markov chain steady state computations, as well as applicationspecific methods for computing multivariate expectations.
PrivacyPreserving Group Data Access via Stateless Oblivious RAM Simulation ∗
"... Motivated by cloud computing applications, we study the problem of providing privacypreserving access to an outsourced honestbutcurious data repository for a group of trusted users. We show how to achieve efficient privacypreserving data access using a combination of probabilistic encryption, wh ..."
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Cited by 61 (8 self)
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Motivated by cloud computing applications, we study the problem of providing privacypreserving access to an outsourced honestbutcurious data repository for a group of trusted users. We show how to achieve efficient privacypreserving data access using a combination of probabilistic encryption, which directly hides data values, and stateless oblivious RAM simulation, which hides the pattern of data accesses. We give a method with O(log n) amortized access overhead for simulating a RAM algorithm that has a memory of size n, using a scheme that is dataoblivious with very high probability. We assume that the simulation has access to a private workspace of size O(nν), for any given fixed constant ν> 0, but does not maintain state in between data access requests. Our simulation makes use of pseudorandom hash functions and is based on a novel hierarchy of cuckoo hash tables that all share a common stash. The method outperforms all previous techniques for stateless clients in terms of access overhead. We also provide experimental results from a prototype implementation of our scheme, showing its practicality. In addition, we show that one can eliminate the dependence on pseudorandom hash functions in our simulation while having the overhead rise to be O(log 2 n). 1
Truthful mechanism design for multidimensional scheduling via cycle monotonicity
 In Proceedings 8th ACM Conference on Electronic Commerce (EC
, 2007
"... We consider the problem of makespan minimization on m unrelated machines in the context of algorithmic mechanism design, where the machines are the strategic players. This is a multidimensional scheduling domain, and the only known positive results for makespan minimization in such a domain are O(m) ..."
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Cited by 50 (12 self)
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We consider the problem of makespan minimization on m unrelated machines in the context of algorithmic mechanism design, where the machines are the strategic players. This is a multidimensional scheduling domain, and the only known positive results for makespan minimization in such a domain are O(m)approximation truthful mechanisms [22, 20]. We study a wellmotivated special case of this problem, where the processing time of a job on each machine may either be “low ” or “high”, and the low and high values are public and jobdependent. This preserves the multidimensionality of the domain, and generalizes the restrictedmachines (i.e., {pj, ∞}) setting in scheduling. We give a general technique to convert any capproximation algorithm to a 3capproximation truthfulinexpectation mechanism. This is one of the few known results that shows how to export approximation
Using combinatorial optimization within maxproduct belief propagation
 Advances in Neural Information Processing Systems (NIPS
, 2007
"... In general, the problem of computing a maximum a posteriori (MAP) assignment in a Markov random field (MRF) is computationally intractable. However, in certain subclasses of MRF, an optimal or closetooptimal assignment can be found very efficiently using combinatorial optimization algorithms: cert ..."
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Cited by 49 (6 self)
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In general, the problem of computing a maximum a posteriori (MAP) assignment in a Markov random field (MRF) is computationally intractable. However, in certain subclasses of MRF, an optimal or closetooptimal assignment can be found very efficiently using combinatorial optimization algorithms: certain MRFs with mutual exclusion constraints can be solved using bipartite matching, and MRFs with regular potentials can be solved using minimum cut methods. However, these solutions do not apply to the many MRFs that contain such tractable components as subnetworks, but also other noncomplying potentials. In this paper, we present a new method, called COMPOSE, for exploiting combinatorial optimization for subnetworks within the context of a maxproduct belief propagation algorithm. COMPOSE uses combinatorial optimization for computing exact maxmarginals for an entire subnetwork; these can then be used for inference in the context of the network as a whole. We describe highly efficient methods for computing maxmarginals for subnetworks corresponding both to bipartite matchings and to regular networks. We present results on both synthetic and real networks encoding correspondence problems between images, which involve both matching constraints and pairwise geometric constraints. We compare to a range of current methods, showing that the ability of COMPOSE to transmit information globally across the network leads to improved convergence, decreased running time, and higherscoring assignments. 1
Practical Verified Computation with Streaming Interactive Proofs
"... When delegating computation to a service provider, as in the cloud computing paradigm, we seek some reassurance that the output is correct and complete. Yet recomputing the output as a check is inefficient and expensive, and it may not even be feasible to store all the data locally. We are therefore ..."
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Cited by 39 (7 self)
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When delegating computation to a service provider, as in the cloud computing paradigm, we seek some reassurance that the output is correct and complete. Yet recomputing the output as a check is inefficient and expensive, and it may not even be feasible to store all the data locally. We are therefore interested in what can be validated by a streaming (sublinear space) user, who cannot store the full input, or perform the full computation herself. Our aim in this work is to advance a recent line of work on “proof systems ” in which the service provider proves the correctness of its output to a user. The goal is to minimize the time and space costs of both parties in generating and checking the proof. Only very recently have there been attempts to implement such proof systems, and thus far these have been quite limited in
Spectrum Auction Framework for Access Allocation in Cognitive Radio Networks
, 2009
"... Cognitive radio networks are emerging as a promising technology for the efficient use of radio spectrum. In these networks, there are two categories of networks on different channels: primary networks and secondary networks. A primary network on a channel has prioritized access to the channel and se ..."
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Cited by 35 (1 self)
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Cognitive radio networks are emerging as a promising technology for the efficient use of radio spectrum. In these networks, there are two categories of networks on different channels: primary networks and secondary networks. A primary network on a channel has prioritized access to the channel and secondary networks can use the channel when the primary network is not using it. The access allocation problem is to select the primary and secondary networks on each channel. We develop an auctionbased framework that allows networks to bid for primary and secondary access based on their utilities and traffic demands, and uses the bids to solve the access allocation problem. We develop algorithms for the access allocation problem and show how they can be used either to maximize the auctioneer’s revenue given the bids, or to maximize the social welfare of the bidding networks, while enforcing incentive compatibility. We first consider the case when the bids of a network depend on which other networks it will share channels with. When there can be only one secondary network on a channel, we design an optimal polynomialtime algorithm for the access allocation problem based on reduction to a maximum matching probleminweightedgraphs. Whentherecanbetwoormore secondary networks on a channel, we show that the optimal access allocation problem is NPComplete. Next, we consider the case when the bids of a network are independent of which other networks it will share channels with. We design a polynomialtime dynamic programming algorithm to optimally solve the access allocation problem when the number of possible cardinalities of the set of secondary networks on a channel is upperbounded. Finally, we design a polynomialtime algorithm which approximates the access allocation problem within a factor of 2 when the above upper bound does not exist.
Solving connectivity problems parameterized by treewidth in single exponential time (Extended Abstract)
, 2011
"... For the vast majority of local problems on graphs of small treewidth (where by local we mean that a solution can be verified by checking separately the neighbourhood of each vertex), standard dynamic programming techniques give c tw V  O(1) time algorithms, where tw is the treewidth of the input g ..."
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Cited by 33 (7 self)
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For the vast majority of local problems on graphs of small treewidth (where by local we mean that a solution can be verified by checking separately the neighbourhood of each vertex), standard dynamic programming techniques give c tw V  O(1) time algorithms, where tw is the treewidth of the input graph G = (V, E) and c is a constant. On the other hand, for problems with a global requirement (usually connectivity) the best–known algorithms were naive dynamic programming schemes running in at least tw tw time. We breach this gap by introducing a technique we named Cut&Count that allows to produce c tw V  O(1) time Monte Carlo algorithms for most connectivitytype problems, including HAMILTONIAN PATH, STEINER TREE, FEEDBACK VERTEX SET and CONNECTED DOMINATING SET. These results have numerous consequences in various fields, like parameterized complexity, exact and approximate algorithms on planar and Hminorfree graphs and exact algorithms on graphs of bounded degree. The constant c in our algorithms is in all cases small, and in several cases we are able to show that improving those constants would cause the Strong Exponential Time Hypothesis to fail. In contrast to the problems aiming to minimize the number of connected components that we solve using Cut&Count as mentioned above, we show that, assuming the Exponential Time Hypothesis, the aforementioned gap cannot be breached for some problems that aim to maximize the number of connected components like CYCLE PACKING.
Beyond TCAMs: An SRAMbased Parallel MultiPipeline Architecture for Terabit IP Lookup
"... Continuous growth in network link rates poses a strong demand on high speed IP lookup engines. While Ternary Content Addressable Memory (TCAM) based solutions serve most of today’s highend routers, they do not scale well for the nextgeneration [1]. On the other hand, pipelined SRAMbased algorithm ..."
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Cited by 27 (11 self)
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Continuous growth in network link rates poses a strong demand on high speed IP lookup engines. While Ternary Content Addressable Memory (TCAM) based solutions serve most of today’s highend routers, they do not scale well for the nextgeneration [1]. On the other hand, pipelined SRAMbased algorithmic solutions become attractive. Intuitively multiple pipelines can be utilized in parallel to have a multiplicative effect on the throughput. However, several challenges must be addressed for such solutions to realize high throughput. First, the memory distribution across different stages of each pipeline as well as across different pipelines must be balanced. Second, the traffic on various pipelines should be balanced. In this paper, we propose a parallel SRAMbased multipipeline architecture for terabit IP lookup. To balance the memory requirement over the stages, a twolevel mapping scheme is presented. By trie partitioning and subtrietopipeline mapping, we ensure that each pipeline contains approximately equal number of trie nodes. Then, within each pipeline, a finegrained nodetostage mapping is used to achieve evenly distributed memory across the stages. To balance the traffic on different pipelines, both pipelined prefix caching and dynamic subtrietopipeline remapping are employed. Simulation using reallife data shows that the proposed architecture with 8 pipelines can store a core routing table with over 200K unique routing prefixes using 3.5 MB of memory. It achieves a throughput of up to 3.2 billion packets per second, i.e. 1 Tbps for minimum size (40 bytes) packets.