911 research outputs found

    Improved Analysis of Deterministic Load-Balancing Schemes

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    We consider the problem of deterministic load balancing of tokens in the discrete model. A set of nn processors is connected into a dd-regular undirected network. In every time step, each processor exchanges some of its tokens with each of its neighbors in the network. The goal is to minimize the discrepancy between the number of tokens on the most-loaded and the least-loaded processor as quickly as possible. Rabani et al. (1998) present a general technique for the analysis of a wide class of discrete load balancing algorithms. Their approach is to characterize the deviation between the actual loads of a discrete balancing algorithm with the distribution generated by a related Markov chain. The Markov chain can also be regarded as the underlying model of a continuous diffusion algorithm. Rabani et al. showed that after time T=O(log(Kn)/μ)T = O(\log (Kn)/\mu), any algorithm of their class achieves a discrepancy of O(dlogn/μ)O(d\log n/\mu), where μ\mu is the spectral gap of the transition matrix of the graph, and KK is the initial load discrepancy in the system. In this work we identify some natural additional conditions on deterministic balancing algorithms, resulting in a class of algorithms reaching a smaller discrepancy. This class contains well-known algorithms, eg., the Rotor-Router. Specifically, we introduce the notion of cumulatively fair load-balancing algorithms where in any interval of consecutive time steps, the total number of tokens sent out over an edge by a node is the same (up to constants) for all adjacent edges. We prove that algorithms which are cumulatively fair and where every node retains a sufficient part of its load in each step, achieve a discrepancy of O(min{dlogn/μ,dn})O(\min\{d\sqrt{\log n/\mu},d\sqrt{n}\}) in time O(T)O(T). We also show that in general neither of these assumptions may be omitted without increasing discrepancy. We then show by a combinatorial potential reduction argument that any cumulatively fair scheme satisfying some additional assumptions achieves a discrepancy of O(d)O(d) almost as quickly as the continuous diffusion process. This positive result applies to some of the simplest and most natural discrete load balancing schemes.Comment: minor corrections; updated literature overvie

    Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks

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    We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPs) in time series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation and a prototype climate model. The LSTM networks outperform the GPs in short-term forecasting accuracy in all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is proposed to ensure convergence to the invariant measure. This novel hybrid method is fully data-driven and extends the forecasting capabilities of LSTM networks.Comment: 31 page

    Statistically-secure ORAM with O~(log2n)\tilde{O}(\log^2 n) Overhead

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    We demonstrate a simple, statistically secure, ORAM with computational overhead O~(log2n)\tilde{O}(\log^2 n); previous ORAM protocols achieve only computational security (under computational assumptions) or require Ω~(log3n)\tilde{\Omega}(\log^3 n) overheard. An additional benefit of our ORAM is its conceptual simplicity, which makes it easy to implement in both software and (commercially available) hardware. Our construction is based on recent ORAM constructions due to Shi, Chan, Stefanov, and Li (Asiacrypt 2011) and Stefanov and Shi (ArXiv 2012), but with some crucial modifications in the algorithm that simplifies the ORAM and enable our analysis. A central component in our analysis is reducing the analysis of our algorithm to a "supermarket" problem; of independent interest (and of importance to our analysis,) we provide an upper bound on the rate of "upset" customers in the "supermarket" problem

    Cryptographic error correction

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (leaves 67-71).It has been said that "cryptography is about concealing information, and coding theory is about revealing it." Despite these apparently conflicting goals, the two fields have common origins and many interesting relationships. In this thesis, we establish new connections between cryptography and coding theory in two ways: first, by applying cryptographic tools to solve classical problems from the theory of error correction; and second, by studying special kinds of codes that are motivated by cryptographic applications. In the first part of this thesis, we consider a model of error correction in which the source of errors is adversarial, but limited to feasible computation. In this model, we construct appealingly simple, general, and efficient cryptographic coding schemes which can recover from much larger error rates than schemes for classical models of adversarial noise. In the second part, we study collusion-secure fingerprinting codes, which are of fundamental importance in cryptographic applications like data watermarking and traitor tracing. We demonstrate tight lower bounds on the lengths of such codes by devising and analyzing a general collusive attack that works for any code.by Christopher Jason Peikert.Ph.D

    Attacks on Geographic Routing Protocols for Wireless Sensor Network

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    With the increase in the military and several other applications of Wireless Sensor Network, provisions must be made for secure transmission of sensitive information throughout the network. Most of the routing protocols proposed for ad-hoc networks and sensor networks are not designed with security as a goal. Hence, many routing protocols are vulnerable to an attack by an adversary who can disrupt the network or harness valuable information from the network. Routing Protocols for wireless sensor networks are classified into three types depending on their network structure as Flat routing protocols, Hierarchical routing protocol and Geographic routing protocols. Large number of nodes in a wireless sensor network , limited battery power and their data centric nature make routing in wireless sensor network a challenging problem. We mainly concentrate on location-based or geographic routing protocol like Greedy Perimeter Stateless Routing Protocol. Sybil attack and Selective forwarding attack are the two attacks feasible in GPSR. These attacks are implemented in GPSR and their losses caused to the network are analysed
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