OpenRaiser/Intern-Atlas huggingface dataset:
Network Control: A Rate-Distortion Perspective
Venue: arXiv cs.IT 2011
Year: 2011

Today's networks are controlled assuming pre-compressed and packetized data. For video, this assumption of data packets abstracts out one of the key aspects - the lossy compression problem. Therefore, first, this paper develops a framework for network control that incorporates both source-rate and source-distortion. Next, it decomposes the network control problem into an application-layer compression control, a transport-layer congestion control and a network-layer scheduling. It is shown that this decomposition is optimal for concave utility functions. Finally, this paper derives further insights from the developed rate-distortion framework by focusing on specific problems.
Free iterative and iteration K-semialgebras
Venue: arXiv cs.FL 2011
Year: 2011

We consider algebras of rational power series over an alphabet $Σ$ with coefficients in a commutative semiring $K$ and characterize them as the free algebras in various classes of algebraic structures.
Approximation Analysis of Influence Spread in Social Networks
Venue: arXiv cs.DM 2011
Year: 2011

In the context of influence propagation in a social graph, we can identify three orthogonal dimensions - the number of seed nodes activated at the beginning (known as budget), the expected number of activated nodes at the end of the propagation (known as expected spread or coverage), and the time taken for the propagation. We can constrain one or two of these and try to optimize the third. In their seminal paper, Kempe et al. constrained the budget, left time unconstrained, and maximized the coverage: this problem is known as Influence Maximization. In this paper, we study alternative optimization problems which are naturally motivated by resource and time constraints on viral marketing campaigns. In the first problem, termed Minimum Target Set Selection (or MINTSS for short), a coverage threshold n is given and the task is to find the minimum size seed set such that by activating it, at least n nodes are eventually activated in the expected sense. In the second problem, termed MINTIME, a coverage threshold n and a budget threshold k are given, and the task is to find a seed set of size at most k such that by activating it, at least n nodes are activated, in the minimum possible time. Both these problems are NP-hard, which motivates our interest in their approximation. For MINTSS, we develop a simple greedy algorithm and show that it provides a bicriteria approximation. We also establish a generic hardness result suggesting that improving it is likely to be hard. For MINTIME, we show that even bicriteria and tricriteria approximations are hard under several conditions. However, if we allow the budget to be boosted by a logarithmic factor and allow the coverage to fall short, then the problem can be solved exactly in PTIME. Finally, we show the value of the approximation algorithms, by comparing them against various heuristics.
Rate-Constrained Simulation and Source Coding IID Sources
Venue: arXiv cs.IT 2011
Year: 2011

Necessary conditions for asymptotically optimal sliding-block or stationary codes for source coding and rate-constrained simulation of memoryless sources are presented and used to motivate a design technique for trellis-encoded source coding and rate-constrained simulation. The code structure has intuitive similarities to classic random coding arguments as well as to ``fake process'' methods and alphabet-constrained methods. Experimental evidence shows that the approach provides comparable or superior performance in comparison with previously published methods on common examples, sometimes by significant margins.
Securing Dynamic Distributed Storage Systems against Eavesdropping and Adversarial Attacks
Venue: arXiv cs.IT 2011
Year: 2011

We address the problem of securing distributed storage systems against eavesdropping and adversarial attacks. An important aspect of these systems is node failures over time, necessitating, thus, a repair mechanism in order to maintain a desired high system reliability. In such dynamic settings, an important security problem is to safeguard the system from an intruder who may come at different time instances during the lifetime of the storage system to observe and possibly alter the data stored on some nodes. In this scenario, we give upper bounds on the maximum amount of information that can be stored safely on the system. For an important operating regime of the distributed storage system, which we call the 'bandwidth-limited regime', we show that our upper bounds are tight and provide explicit code constructions. Moreover, we provide a way to short list the malicious nodes and expurgate the system.
Loss Rate Inference in Multi-Sources and Multicast-Based General Topology
Venue: arXiv cs.NI 2011
Year: 2011

Loss tomography has received considerable attention in recent years and a number of estimators have been proposed. Unfortunately, almost all of them are devoted to the tree topology despite the general topology is more common in practice. In addition, most of the works presented in the literature rely on iterative approximation to search for the maximum of a likelihood function formed from observations, which have been known neither scalable nor efficient. In contrast to the tree topology, there is few paper dedicated to the general topology because of the lack of understanding the impacts created by the probes sent by different sources. We in this paper present the analytical results obtained recently for the general topology that show the correlation created by the probes sent by multiple sources to a node located in an intersection of multiple trees. The correlation is expressed by a set of polynomials of the pass rates of the paths connecting the sources to the node. In addition to the expression, a closed form solution is proposed to obtain the MLE of the pass rates of the paths connecting the sources to the node. Then, two strategies are proposed to estimate the loss rate of a link for the general topology: one is path-based and the other is link-based, depending on whether we need to obtain the pass rate of a path first. The two strategies are compared in the context of the general topology that shows each has its advantages and the link-based one is more general. Apart from proving the estimates obtained are the MLEs, we prove the estimator presented here has the optimal asymptotic property.
Secret Sharing LDPC Codes for the BPSK-constrained Gaussian Wiretap Channel
Venue: arXiv cs.IT 2011
Year: 2011

The problem of secret sharing over the Gaussian wiretap channel is considered. A source and a destination intend to share secret information over a Gaussian channel in the presence of a wiretapper who observes the transmission through another Gaussian channel. Two constraints are imposed on the source-to-destination channel; namely, the source can transmit only binary phase shift keyed (BPSK) symbols, and symbol-by-symbol hard-decision quantization is applied to the received symbols of the destination. An error-free public channel is also available for the source and destination to exchange messages in order to help the secret sharing process. The wiretapper can perfectly observe all messages in the public channel. It is shown that a secret sharing scheme that employs a random ensemble of regular low density parity check (LDPC) codes can achieve the key capacity of the BPSK-constrained Gaussian wiretap channel asymptotically with increasing block length. To accommodate practical constraints of finite block length and limited decoding complexity, fixed irregular LDPC codes are also designed to replace the regular LDPC code ensemble in the proposed secret sharing scheme.
Strong Secrecy on the Binary Erasure Wiretap Channel Using Large-Girth LDPC Codes
Venue: arXiv cs.IT 2011
Year: 2011

For an arbitrary degree distribution pair (DDP), we construct a sequence of low-density parity-check (LDPC) code ensembles with girth growing logarithmically in block-length using Ramanujan graphs. When the DDP has minimum left degree at least three, we show using density evolution analysis that the expected bit-error probability of these ensembles, when passed through a binary erasure channel with erasure probability $ε$, decays as $\mathcal{O}(\exp(-c_1 n^{c_2}))$ with the block-length $n$ for positive constants $c_1$ and $c_2$, as long as $ε$ is lesser than the erasure threshold $ε_\mathrm{th}$ of the DDP. This guarantees that the coset coding scheme using the dual sequence provides strong secrecy over the binary erasure wiretap channel for erasure probabilities greater than $1 - ε_\mathrm{th}$.
A Unified View of Regularized Dual Averaging and Mirror Descent with Implicit Updates
Venue: arXiv cs.LG 2011
Year: 2011

We study three families of online convex optimization algorithms: follow-the-proximally-regularized-leader (FTRL-Proximal), regularized dual averaging (RDA), and composite-objective mirror descent. We first prove equivalence theorems that show all of these algorithms are instantiations of a general FTRL update. This provides theoretical insight on previous experimental observations. In particular, even though the FOBOS composite mirror descent algorithm handles L1 regularization explicitly, it has been observed that RDA is even more effective at producing sparsity. Our results demonstrate that FOBOS uses subgradient approximations to the L1 penalty from previous rounds, leading to less sparsity than RDA, which handles the cumulative penalty in closed form. The FTRL-Proximal algorithm can be seen as a hybrid of these two, and outperforms both on a large, real-world dataset. Our second contribution is a unified analysis which produces regret bounds that match (up to logarithmic terms) or improve the best previously known bounds. This analysis also extends these algorithms in two important ways: we support a more general type of composite objective and we analyze implicit updates, which replace the subgradient approximation of the current loss function with an exact optimization.
Distributed STBCs with Full-diversity Partial Interference Cancellation Decoding
Venue: arXiv cs.IT 2011
Year: 2011

Recently, Guo and Xia introduced low complexity decoders called Partial Interference Cancellation (PIC) and PIC with Successive Interference Cancellation (PIC-SIC), which include the Zero Forcing (ZF) and ZF-SIC receivers as special cases, for point-to-point MIMO channels. In this paper, we show that PIC and PIC-SIC decoders are capable of achieving the full cooperative diversity available in wireless relay networks. We give sufficient conditions for a Distributed Space-Time Block Code (DSTBC) to achieve full diversity with PIC and PIC-SIC decoders and construct a new class of DSTBCs with low complexity full-diversity PIC-SIC decoding using complex orthogonal designs. The new class of codes includes a number of known full-diversity PIC/PIC-SIC decodable Space-Time Block Codes (STBCs) constructed for point-to-point channels as special cases. The proposed DSTBCs achieve higher rates (in complex symbols per channel use) than the multigroup ML decodable DSTBCs available in the literature. Simulation results show that the proposed codes have better bit error rate performance than the best known low complexity, full-diversity DSTBCs.
Improving PPSZ for 3-SAT using Critical Variables
Venue: arXiv cs.DS 2011
Year: 2011

A critical variable of a satisfiable CNF formula is a variable that has the same value in all satisfying assignments. Using a simple case distinction on the fraction of critical variables of a CNF formula, we improve the running time for 3-SAT from O(1.32216^n) by Rolf [2006] to O(1.32153^n). Using a different approach, Iwama et al. [2010] very recently achieved a running time of O(1.32113^n). Our method nicely combines with theirs, yielding the currently fastest known algorithm with running time O(1.32065^n). We also improve the bound for 4-SAT from O(1.47390^n) [Iwama, Tamaki 2004] to O(1.46928^n), where O(1.46981^n) can be obtained using the methods of [Iwama, Tamaki 2004] and [Rolf 2006].
Efficient Clustering with Limited Distance Information
Venue: arXiv cs.DS 2011
Year: 2011

Given a point set S and an unknown metric d on S, we study the problem of efficiently partitioning S into k clusters while querying few distances between the points. In our model we assume that we have access to one versus all queries that given a point s in S return the distances between s and all other points. We show that given a natural assumption about the structure of the instance, we can efficiently find an accurate clustering using only O(k) distance queries. Our algorithm uses an active selection strategy to choose a small set of points that we call landmarks, and considers only the distances between landmarks and other points to produce a clustering. We use our algorithm to cluster proteins by sequence similarity. This setting nicely fits our model because we can use a fast sequence database search program to query a sequence against an entire dataset. We conduct an empirical study that shows that even though we query a small fraction of the distances between the points, we produce clusterings that are close to a desired clustering given by manual classification.
Portfolio Allocation for Bayesian Optimization
Venue: arXiv cs.LG 2011
Year: 2011

Bayesian optimization with Gaussian processes has become an increasingly popular tool in the machine learning community. It is efficient and can be used when very little is known about the objective function, making it popular in expensive black-box optimization scenarios. It uses Bayesian methods to sample the objective efficiently using an acquisition function which incorporates the model's estimate of the objective and the uncertainty at any given point. However, there are several different parameterized acquisition functions in the literature, and it is often unclear which one to use. Instead of using a single acquisition function, we adopt a portfolio of acquisition functions governed by an online multi-armed bandit strategy. We propose several portfolio strategies, the best of which we call GP-Hedge, and show that this method outperforms the best individual acquisition function. We also provide a theoretical bound on the algorithm's performance.
Interference Alignment as a Rank Constrained Rank Minimization
Venue: arXiv cs.IT 2011
Year: 2011

We show that the maximization of the sum degrees-of-freedom for the static flat-fading multiple-input multiple-output (MIMO) interference channel is equivalent to a rank constrained rank minimization problem (RCRM), when the signal spaces span all available dimensions. The rank minimization corresponds to maximizing interference alignment (IA) so that interference spans the lowest dimensional subspace possible. The rank constraints account for the useful signal spaces spanning all available spatial dimensions. That way, we reformulate all IA requirements to requirements involving ranks. Then, we present a convex relaxation of the RCRM problem inspired by recent results in compressed sensing and low-rank matrix completion theory that rely on approximating rank with the nuclear norm. We show that the convex envelope of the sum of ranks of the interference matrices is the normalized sum of their corresponding nuclear norms and introduce tractable constraints that are asymptotically equivalent to the rank constraints for the initial problem. We also show that our heuristic relaxation can be tuned for the multi-cell interference channel. Furthermore, we experimentally show that in many cases the proposed algorithm attains perfect interference alignment and in some cases outperforms previous approaches for finding precoding and zero-forcing matrices for interference alignment.
Searching in Dynamic Tree-Like Partial Orders
Venue: arXiv cs.DS 2011
Year: 2011

We give the first data structure for the problem of maintaining a dynamic set of n elements drawn from a partially ordered universe described by a tree. We define the Line-Leaf Tree, a linear-sized data structure that supports the operations: insert; delete; test membership; and predecessor. The performance of our data structure is within an O(log w)-factor of optimal. Here w <= n is the width of the partial-order---a natural obstacle in searching a partial order.
Weight Distributions of Regular Low-Density Parity-Check Codes over Finite Fields
Venue: arXiv cs.IT 2011
Year: 2011

The average weight distribution of a regular low-density parity-check (LDPC) code ensemble over a finite field is thoroughly analyzed. In particular, a precise asymptotic approximation of the average weight distribution is derived for the small-weight case, and a series of fundamental qualitative properties of the asymptotic growth rate of the average weight distribution are proved. Based on this analysis, a general result, including all previous results as special cases, is established for the minimum distance of individual codes in a regular LDPC code ensemble.
Information-based complexity, feedback and dynamics in convex programming
Venue: arXiv cs.IT 2011
Year: 2011

We study the intrinsic limitations of sequential convex optimization through the lens of feedback information theory. In the oracle model of optimization, an algorithm queries an {\em oracle} for noisy information about the unknown objective function, and the goal is to (approximately) minimize every function in a given class using as few queries as possible. We show that, in order for a function to be optimized, the algorithm must be able to accumulate enough information about the objective. This, in turn, puts limits on the speed of optimization under specific assumptions on the oracle and the type of feedback. Our techniques are akin to the ones used in statistical literature to obtain minimax lower bounds on the risks of estimation procedures; the notable difference is that, unlike in the case of i.i.d. data, a sequential optimization algorithm can gather observations in a {\em controlled} manner, so that the amount of information at each step is allowed to change in time. In particular, we show that optimization algorithms often obey the law of diminishing returns: the signal-to-noise ratio drops as the optimization algorithm approaches the optimum. To underscore the generality of the tools, we use our approach to derive fundamental lower bounds for a certain active learning problem. Overall, the present work connects the intuitive notions of information in optimization, experimental design, estimation, and active learning to the quantitative notion of Shannon information.
Recovering Compressively Sampled Signals Using Partial Support Information
Venue: arXiv cs.IT 2011
Year: 2011

In this paper we study recovery conditions of weighted $\ell_1$ minimization for signal reconstruction from compressed sensing measurements when partial support information is available. We show that if at least 50% of the (partial) support information is accurate, then weighted $\ell_1$ minimization is stable and robust under weaker conditions than the analogous conditions for standard $\ell_1$ minimization. Moreover, weighted $\ell_1$ minimization provides better bounds on the reconstruction error in terms of the measurement noise and the compressibility of the signal to be recovered. We illustrate our results with extensive numerical experiments on synthetic data and real audio and video signals.
Controller Synthesis for Safety and Reachability via Approximate Bisimulation
Venue: arXiv cs.SY 2011
Year: 2011

In this paper, we consider the problem of controller design using approximately bisimilar abstractions with an emphasis on safety and reachability specifications. We propose abstraction-based approaches to solve both classes of problems. We start by synthesizing a controller for an approximately bisimilar abstraction. Then, using a concretization procedure, we obtain a controller for our initial system that is proved "correct by design". We provide guarantees of performance by giving estimates of the distance of the synthesized controller to the maximal (i.e the most permissive) safety controller or to the time-optimal reachability controller. Finally, we use the presented techniques combined with discrete approximately bisimilar abstractions of switched systems developed recently, for switching controller synthesis.
A Bio-Inspired Robust Adaptive Random Search Algorithm for Distributed Beamforming
Venue: arXiv cs.IT 2011
Year: 2011

A bio-inspired robust adaptive random search algorithm (BioRARSA), designed for distributed beamforming for sensor and relay networks, is proposed in this work. It has been shown via a systematic framework that BioRARSA converges in probability and its convergence time scales linearly with the number of distributed transmitters. More importantly, extensive simulation results demonstrate that the proposed BioRARSA outperforms existing adaptive distributed beamforming schemes by as large as 29.8% on average. This increase in performance results from the fact that BioRARSA can adaptively adjust its sampling stepsize via the "swim" behavior inspired by the bacterial foraging mechanism. Hence, the convergence time of BioRARSA is insensitive to the initial sampling stepsize of the algorithm, which makes it robust against the dynamic nature of distributed wireless networks.
Independent sets in random graphs from the weighted second moment method
Venue: arXiv cs.CC 2011
Year: 2011

We prove new lower bounds on the likely size of a maximum independent set in a random graph with a given average degree. Our method is a weighted version of the second moment method, where we give each independent set a weight based on the total degree of its vertices.
Algorithmic Verification of Asynchronous Programs
Venue: arXiv cs.LO 2011
Year: 2011

Asynchronous programming is a ubiquitous systems programming idiom to manage concurrent interactions with the environment. In this style, instead of waiting for time-consuming operations to complete, the programmer makes a non-blocking call to the operation and posts a callback task to a task buffer that is executed later when the time-consuming operation completes. A co-operative scheduler mediates the interaction by picking and executing callback tasks from the task buffer to completion (and these callbacks can post further callbacks to be executed later). Writing correct asynchronous programs is hard because the use of callbacks, while efficient, obscures program control flow. We provide a formal model underlying asynchronous programs and study verification problems for this model. We show that the safety verification problem for finite-data asynchronous programs is expspace-complete. We show that liveness verification for finite-data asynchronous programs is decidable and polynomial-time equivalent to Petri Net reachability. Decidability is not obvious, since even if the data is finite-state, asynchronous programs constitute infinite-state transition systems: both the program stack and the task buffer of pending asynchronous calls can be potentially unbounded. Our main technical construction is a polynomial-time semantics-preserving reduction from asynchronous programs to Petri Nets and conversely. The reduction allows the use of algorithmic techniques on Petri Nets to the verification of asynchronous programs. We also study several extensions to the basic models of asynchronous programs that are inspired by additional capabilities provided by implementations of asynchronous libraries, and classify the decidability and undecidability of verification questions on these extensions.