OpenRaiser/Intern-Atlas huggingface dataset:
Algorithm 950: Ncpol2sdpa---Sparse Semidefinite Programming Relaxations for Polynomial Optimization Problems of Noncommuting Variables
Venue: arXiv cs.MS 2015
Year: 2015

A hierarchy of semidefinite programming (SDP) relaxations approximates the global optimum of polynomial optimization problems of noncommuting variables. Generating the relaxation, however, is a computationally demanding task, and only problems of commuting variables have efficient generators. We develop an implementation for problems of noncommuting problems that creates the relaxation to be solved by SDPA -- a high-performance solver that runs in a distributed environment. We further exploit the inherent sparsity of optimization problems in quantum physics to reduce the complexity of the resulting relaxations. Constrained problems with a relaxation of order two may contain up to a hundred variables. The implementation is available in Python. The tool helps solve problems such as finding the ground state energy or testing quantum correlations.
PDA: Semantically Secure Time-Series Data Analytics with Dynamic Subgroups
Venue: arXiv cs.CR 2015
Year: 2015

Third-party analysis on private records is becoming increasingly important due to the widespread data collection for various analysis purposes. However, the data in its original form often contains sensitive information about individuals, and its publication will severely breach their privacy. In this paper, we present a novel Privacy-preserving Data Analytics framework PDA, which allows a third-party aggregator to obliviously conduct many different types of polynomial-based analysis on private data records provided by a dynamic sub-group of users. Notably, every user needs to keep only O(n) keys to join data analysis among O(2^n) different groups of users, and any data analysis that is represented by polynomials is supported by our framework. Besides, a real implementation shows the performance of our framework is comparable to the peer works who present ad-hoc solutions for specific data analysis applications. Despite such nice properties of PDA, it is provably secure against a very powerful attacker (chosen-plaintext attack) even in the Dolev-Yao network model where all communication channels are insecure.
Enabling Privacy-preserving Auctions in Big Data
Venue: arXiv cs.CR 2015
Year: 2015

We study how to enable auctions in the big data context to solve many upcoming data-based decision problems in the near future. We consider the characteristics of the big data including, but not limited to, velocity, volume, variety, and veracity, and we believe any auction mechanism design in the future should take the following factors into consideration: 1) generality (variety); 2) efficiency and scalability (velocity and volume); 3) truthfulness and verifiability (veracity). In this paper, we propose a privacy-preserving construction for auction mechanism design in the big data, which prevents adversaries from learning unnecessary information except those implied in the valid output of the auction. More specifically, we considered one of the most general form of the auction (to deal with the variety), and greatly improved the the efficiency and scalability by approximating the NP-hard problems and avoiding the design based on garbled circuits (to deal with velocity and volume), and finally prevented stakeholders from lying to each other for their own benefit (to deal with the veracity). We achieve these by introducing a novel privacy-preserving winner determination algorithm and a novel payment mechanism. Additionally, we further employ a blind signature scheme as a building block to let bidders verify the authenticity of their payment reported by the auctioneer. The comparison with peer work shows that we improve the asymptotic performance of peer works' overhead from the exponential growth to a linear growth and from linear growth to a logarithmic growth, which greatly improves the scalability.
The complexity of Shortest Common Supersequence for inputs with no identical consecutive letters
Venue: arXiv cs.DM 2015
Year: 2015

The Shortest Common Supersequence problem (SCS for short) consists in finding a shortest common supersequence of a finite set of words on a fixed alphabet Sigma. It is well-known that its decision version denoted [SR8] in [Garey and Johnson] is NP-complete. Many variants have been studied in the literature. In this paper we settle the complexity of two such variants of SCS where inputs do not contain identical consecutive letters. We prove that those variants denoted φSCS and MSCS both have a decision version which remains NP-complete when |Σ| is at least 3. Note that it was known for MSCS when |Σ| is at least 4 [Fleisher and Woeginger] and we discuss how [Darte] states a similar result for |Σ| at least 3.
Faithful Implementations of Distributed Algorithms and Control Laws
Venue: arXiv cs.GT 2015
Year: 2015

When a distributed algorithm must be executed by strategic agents with misaligned interests, a social leader needs to introduce an appropriate tax/subsidy mechanism to incentivize agents to faithfully implement the intended algorithm so that a correct outcome is obtained. We discuss the incentive issues of implementing economically efficient distributed algorithms using the framework of indirect mechanism design theory. In particular, we show that indirect Groves mechanisms are not only sufficient but also necessary to achieve incentive compatibility. This result can be viewed as a generalization of the Green-Laffont theorem to indirect mechanisms. Then we introduce the notion of asymptotic incentive compatibility as an appropriate solution concept to faithfully implement distributed and iterative optimization algorithms. We consider two special types of optimization algorithms: dual decomposition algorithms for resource allocation and average consensus algorithms.
Meet Your Expectations With Guarantees: Beyond Worst-Case Synthesis in Quantitative Games
Venue: arXiv cs.GT 2015
Year: 2015

We extend the quantitative synthesis framework by going beyond the worst-case. On the one hand, classical analysis of two-player games involves an adversary (modeling the environment of the system) which is purely antagonistic and asks for strict guarantees. On the other hand, stochastic models like Markov decision processes represent situations where the system is faced to a purely randomized environment: the aim is then to optimize the expected payoff, with no guarantee on individual outcomes. We introduce the beyond worst-case synthesis problem, which is to construct strategies that guarantee some quantitative requirement in the worst-case while providing an higher expected value against a particular stochastic model of the environment given as input. This problem is relevant to produce system controllers that provide nice expected performance in the everyday situation while ensuring a strict (but relaxed) performance threshold even in the event of very bad (while unlikely) circumstances. We study the beyond worst-case synthesis problem for two important quantitative settings: the mean-payoff and the shortest path. In both cases, we show how to decide the existence of finite-memory strategies satisfying the problem and how to synthesize one if one exists. We establish algorithms and we study complexity bounds and memory requirements.
Creative Gardens
Venue: arXiv cs.CY 2015
Year: 2015

Can we move beyond simply networking creative individuals to establishing diverse communities of practice for innovation through discursive methods. Furthermore, can we digitise their creativity activities within an integrative socio-cultural collaborative technology platform that could then support distributed innovation. First, we consider the complexity of creative cultures from the perspective of design innovation, including how to nurture creativity activities in what we call Creative Gardens. Specifically, how they could grow, diverge, and combine, be- ing cultivated to nurture emergent, disruptive, collaborative innovation. Then, we consider the digitisation of Creative Gardens from the perspective of digital culture. Specifically, the tenets of Creative Gardens as dynamic and innovative communities. This includes considering the challenges and opportunities around digitisation, the influences around the connectivity with knowledge cultivation, and the potential for distributed innovation as collective intelligence to utilise diverse expertise. We conclude be considering the importance of the issues and questions raised, and their potential for the future.
Incoherence-Optimal Matrix Completion
Venue: arXiv cs.IT 2015
Year: 2015

This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample complexity bound that is order-wise optimal with respect to the incoherence parameter (as well as to the rank $r$ and the matrix dimension $n$ up to a log factor). As a consequence, we improve the sample complexity of recovering a semidefinite matrix from $O(nr^{2}\log^{2}n)$ to $O(nr\log^{2}n)$, and the highest allowable rank from $Θ(\sqrt{n}/\log n)$ to $Θ(n/\log^{2}n)$. The key step in proof is to obtain new bounds on the $\ell_{\infty,2}$-norm, defined as the maximum of the row and column norms of a matrix. To illustrate the applicability of our techniques, we discuss extensions to SVD projection, structured matrix completion and semi-supervised clustering, for which we provide order-wise improvements over existing results. Finally, we turn to the closely-related problem of low-rank-plus-sparse matrix decomposition. We show that the joint incoherence condition is unavoidable here for polynomial-time algorithms conditioned on the Planted Clique conjecture. This means it is intractable in general to separate a rank-$ω(\sqrt{n})$ positive semidefinite matrix and a sparse matrix. Interestingly, our results show that the standard and joint incoherence conditions are associated respectively with the information (statistical) and computational aspects of the matrix decomposition problem.
Approximate String Matching using a Bidirectional Index
Venue: arXiv cs.DS 2015
Year: 2015

We study strategies of approximate pattern matching that exploit bidirectional text indexes, extending and generalizing ideas of Lam et al. We introduce a formalism, called search schemes, to specify search strategies of this type, then develop a probabilistic measure for the efficiency of a search scheme, prove several combinatorial results on efficient search schemes, and finally, provide experimental computations supporting the superiority of our strategies.
An Extension of Cook's Elastic Cipher
Venue: arXiv cs.IT 2015
Year: 2015

Given a block cipher of length L Cook's elastic cipher allows to encrypt messages of variable length from L to 2L. Given some conditions on the key schedule, Cook's elastic cipher is secure against any key recovery attack if the underlying block cipher is, and it achieves complete diffusion in at most q + 1 rounds if the underlying block cipher achieves it in q rounds. We extend Cook's construction inductively, obtaining an elastic cipher for any message length greater than L with the same properties of security as Cook's elastic cipher.
A Faster Algorithm to Recognize Even-Hole-Free Graphs
Venue: arXiv cs.DS 2015
Year: 2015

We study the problem of determining whether an $n$-node graph $G$ has an even hole, i.e., an induced simple cycle consisting of an even number of nodes. Conforti, Cornuéjols, Kapoor, and Vušković gave the first polynomial-time algorithm for the problem, which runs in $O(n^{40})$ time. Later, Chudnovsky, Kawarabayashi, and Seymour reduced the running time to $O(n^{31})$. The best previously known algorithm for the problem, due to da Silva and Vušković, runs in $O(n^{19})$ time. In this paper, we solve the problem in $O(n^{11})$ time. Moreover, if $G$ has even holes, our algorithm also outputs an even hole of $G$ in $O(n^{11})$ time.
On Known-Plaintext Attacks to a Compressed Sensing-based Encryption: A Quantitative Analysis
Venue: arXiv cs.IT 2015
Year: 2015

Despite the linearity of its encoding, compressed sensing may be used to provide a limited form of data protection when random encoding matrices are used to produce sets of low-dimensional measurements (ciphertexts). In this paper we quantify by theoretical means the resistance of the least complex form of this kind of encoding against known-plaintext attacks. For both standard compressed sensing with antipodal random matrices and recent multiclass encryption schemes based on it, we show how the number of candidate encoding matrices that match a typical plaintext-ciphertext pair is so large that the search for the true encoding matrix inconclusive. Such results on the practical ineffectiveness of known-plaintext attacks underlie the fact that even closely-related signal recovery under encoding matrix uncertainty is doomed to fail. Practical attacks are then exemplified by applying compressed sensing with antipodal random matrices as a multiclass encryption scheme to signals such as images and electrocardiographic tracks, showing that the extracted information on the true encoding matrix from a plaintext-ciphertext pair leads to no significant signal recovery quality increase. This theoretical and empirical evidence clarifies that, although not perfectly secure, both standard compressed sensing and multiclass encryption schemes feature a noteworthy level of security against known-plaintext attacks, therefore increasing its appeal as a negligible-cost encryption method for resource-limited sensing applications.
Sparse Phase Retrieval: Uniqueness Guarantees and Recovery Algorithms
Venue: arXiv cs.IT 2015
Year: 2015

The problem of signal recovery from its Fourier transform magnitude is of paramount importance in various fields of engineering and has been around for over 100 years. Due to the absence of phase information, some form of additional information is required in order to be able to uniquely identify the signal of interest. In this work, we focus our attention on discrete-time sparse signals (of length $n$). We first show that, if the DFT dimension is greater than or equal to $2n$, almost all signals with {\em aperiodic} support can be uniquely identified by their Fourier transform magnitude (up to time-shift, conjugate-flip and global phase). Then, we develop an efficient Two-stage Sparse Phase Retrieval algorithm (TSPR), which involves: (i) identifying the support, i.e., the locations of the non-zero components, of the signal using a combinatorial algorithm (ii) identifying the signal values in the support using a convex algorithm. We show that TSPR can {\em provably} recover most $O(n^{1/2-\eps})$-sparse signals (up to a time-shift, conjugate-flip and global phase). We also show that, for most $O(n^{1/4-\eps})$-sparse signals, the recovery is {\em robust} in the presence of measurement noise. Numerical experiments complement our theoretical analysis and verify the effectiveness of TSPR.
Breathe before Speaking: Efficient Information Dissemination Despite Noisy, Limited and Anonymous Communication
Venue: arXiv cs.DC 2015
Year: 2015

Distributed computing models typically assume reliable communication between processors. While such assumptions often hold for engineered networks, e.g., due to underlying error correction protocols, their relevance to biological systems, wherein messages are often distorted before reaching their destination, is quite limited. In this study we take a first step towards reducing this gap by rigorously analyzing a model of communication in large anonymous populations composed of simple agents which interact through short and highly unreliable messages. We focus on the broadcast problem and the majority-consensus problem. Both are fundamental information dissemination problems in distributed computing, in which the goal of agents is to converge to some prescribed desired opinion. We initiate the study of these problems in the presence of communication noise. Our model for communication is extremely weak and follows the push gossip communication paradigm: In each round each agent that wishes to send information delivers a message to a random anonymous agent. This communication is further restricted to contain only one bit (essentially representing an opinion). Lastly, the system is assumed to be so noisy that the bit in each message sent is flipped independently with probability $1/2-ε$, for some small $ε>0$. Even in this severely restricted, stochastic and noisy setting we give natural protocols that solve the noisy broadcast and the noisy majority-consensus problems efficiently. Our protocols run in $O(\log n / ε^2)$ rounds and use $O(n \log n / ε^2)$ messages/bits in total, where $n$ is the number of agents. These bounds are asymptotically optimal and, in fact, are as fast and message efficient as if each agent would have been simultaneously informed directly by an agent that knows the prescribed desired opinion.
Compressive Measurements Generated by Structurally Random Matrices: Asymptotic Normality and Quantization
Venue: arXiv cs.IT 2015
Year: 2015

Structurally random matrices (SRMs) are a practical alternative to fully random matrices (FRMs) when generating compressive sensing measurements because of their computational efficiency and their universality with respect to the sparsifing basis. In this work we derive the statistical distribution of compressive measurements generated by various types of SRMs, as a function of the signal properties. We show that under a wide range of conditions, that distribution is a mixture of asymptotically multi-variate normal components. We point out the implications for quantization and coding of the measurements and discuss design consideration for measurements transmission systems. Simulations on real-world video signals confirm the theoretical findings and show that the signal randomization of SRMs yields a dramatic improvement in quantization properties.
Robust Compressed Sensing Under Matrix Uncertainties
Venue: arXiv cs.IT 2015
Year: 2015

Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be known exactly in advance. However, uncertainties exist due to sampling distortion, finite grids of the parameter space of dictionary, etc. In this paper, we take a generalized sparse signal model, which simultaneously considers the sampling and representation matrix uncertainties. Based on the new signal model, a new optimization model for robust sparse signal reconstruction is proposed. This optimization model can be deduced with stochastic robust approximation analysis. Both convex relaxation and greedy algorithms are used to solve the optimization problem. For the convex relaxation method, a sufficient condition for recovery by convex relaxation is given; For the greedy algorithm, it is realized by the introduction of a pre-processing of the sensing matrix and the measurements. In numerical experiments, both simulated data and real-life ECG data based results show that the proposed method has a better performance than the current methods.
Joint Source-Channel Coding with Time-Varying Channel and Side-Information
Venue: arXiv cs.IT 2015
Year: 2015

Transmission of a Gaussian source over a time-varying Gaussian channel is studied in the presence of time-varying correlated side information at the receiver. A block fading model is considered for both the channel and the side information, whose states are assumed to be known only at the receiver. The optimality of separate source and channel coding in terms of average end-to-end distortion is shown when the channel is static while the side information state follows a discrete or a continuous and quasiconcave distribution. When both the channel and side information states are time-varying, separate source and channel coding is suboptimal in general. A partially informed encoder lower bound is studied by providing the channel state information to the encoder. Several achievable transmission schemes are proposed based on uncoded transmission, separate source and channel coding, joint decoding as well as hybrid digital-analog transmission. Uncoded transmission is shown to be optimal for a class of continuous and quasiconcave side information state distributions, while the channel gain may have an arbitrary distribution. To the best of our knowledge, this is the first example in which the uncoded transmission achieves the optimal performance thanks to the time-varying nature of the states, while it is suboptimal in the static version of the same problem. Then, the optimal \emph{distortion exponent}, that quantifies the exponential decay rate of the expected distortion in the high SNR regime, is characterized for Nakagami distributed channel and side information states, and it is shown to be achieved by hybrid digital-analog and joint decoding schemes in certain cases, illustrating the suboptimality of pure digital or analog transmission in general.
TRAIL: Topology Authentication in RPL
Venue: arXiv cs.NI 2015
Year: 2015

The IPv6 Routing Protocol for Low-Power and Lossy Networks (RPL) was recently introduced as the new routing standard for the Internet of Things. Although RPL defines basic security modes, it remains vulnerable to topological attacks which facilitate blackholing, interception, and resource exhaustion. We are concerned with analyzing the corresponding threats and protecting future RPL deployments from such attacks. Our contributions are twofold. First, we analyze the state of the art, in particular the protective scheme VeRA and present two new rank order attacks as well as extensions to mitigate them. Second, we derive and evaluate TRAIL, a generic scheme for topology authentication in RPL. TRAIL solely relies on the basic assumptions of RPL that (1) the root node serves as a trust anchor and (2) each node interconnects to the root as part of a hierarchy. Using proper reachability tests, TRAIL scalably and reliably identifies any topological attacker without strong cryptographic efforts.
Transmission of a continuous signal via one-bit capacity channel
Venue: arXiv cs.IT 2015
Year: 2015

We study the problem of the transmission of currently observed time variable signals via a channel that is capable of sending a single binary signal only for each measurement of the underlying process. For encoding and decoding, we suggest a modification othe adaptive delta modulation algorithm. This modification ensures tracking of time variable signals. We obtained upper estimates for the error for the case of noiseless transmission.