OpenRaiser/Intern-Atlas huggingface dataset:
Interprocedural Reachability for Flat Integer Programs
Venue: arXiv cs.FL 2015
Year: 2015

We study programs with integer data, procedure calls and arbitrary call graphs. We show that, whenever the guards and updates are given by octagonal relations, the reachability problem along control flow paths within some language w1* ... wd* over program statements is decidable in Nexptime. To achieve this upper bound, we combine a program transformation into the same class of programs but without procedures, with an Np-completeness result for the reachability problem of procedure-less programs. Besides the program, the expression w1* ... wd* is also mapped onto an expression of a similar form but this time over the transformed program statements. Several arguments involving context-free grammars and their generative process enable us to give tight bounds on the size of the resulting expression. The currently existing gap between Np-hard and Nexptime can be closed to Np-complete when a certain parameter of the analysis is assumed to be constant.
Dissipation of information in channels with input constraints
Venue: arXiv cs.IT 2015
Year: 2015

One of the basic tenets in information theory, the data processing inequality states that output divergence does not exceed the input divergence for any channel. For channels without input constraints, various estimates on the amount of such contraction are known, Dobrushin's coefficient for the total variation being perhaps the most well-known. This work investigates channels with average input cost constraint. It is found that while the contraction coefficient typically equals one (no contraction), the information nevertheless dissipates. A certain non-linear function, the \emph{Dobrushin curve} of the channel, is proposed to quantify the amount of dissipation. Tools for evaluating the Dobrushin curve of additive-noise channels are developed based on coupling arguments. Some basic applications in stochastic control, uniqueness of Gibbs measures and fundamental limits of noisy circuits are discussed. As an application, it shown that in the chain of $n$ power-constrained relays and Gaussian channels the end-to-end mutual information and maximal squared correlation decay as $Θ(\frac{\log\log n}{\log n})$, which is in stark contrast with the exponential decay in chains of discrete channels. Similarly, the behavior of noisy circuits (composed of gates with bounded fan-in) and broadcasting of information on trees (of bounded degree) does not experience threshold behavior in the signal-to-noise ratio (SNR). Namely, unlike the case of discrete channels, the probability of bit error stays bounded away from $1\over 2$ regardless of the SNR.
Compressive Imaging via Approximate Message Passing with Image Denoising
Venue: arXiv cs.IT 2015
Year: 2015

We consider compressive imaging problems, where images are reconstructed from a reduced number of linear measurements. Our objective is to improve over existing compressive imaging algorithms in terms of both reconstruction error and runtime. To pursue our objective, we propose compressive imaging algorithms that employ the approximate message passing (AMP) framework. AMP is an iterative signal reconstruction algorithm that performs scalar denoising at each iteration; in order for AMP to reconstruct the original input signal well, a good denoiser must be used. We apply two wavelet based image denoisers within AMP. The first denoiser is the "amplitude-scaleinvariant Bayes estimator" (ABE), and the second is an adaptive Wiener filter; we call our AMP based algorithms for compressive imaging AMP-ABE and AMP-Wiener. Numerical results show that both AMP-ABE and AMP-Wiener significantly improve over the state of the art in terms of runtime. In terms of reconstruction quality, AMP-Wiener offers lower mean square error (MSE) than existing compressive imaging algorithms. In contrast, AMP-ABE has higher MSE, because ABE does not denoise as well as the adaptive Wiener filter.
Capacity of a Class of State-Dependent Orthogonal Relay Channels
Venue: arXiv cs.IT 2015
Year: 2015

The class of orthogonal relay channels in which the orthogonal channels connecting the source terminal to the relay and the destination, and the relay to the destination, depend on a state sequence, is considered. It is assumed that the state sequence is fully known at the destination while it is not known at the source or the relay. The capacity of this class of relay channels is characterized, and shown to be achieved by the partial decode-compress-and-forward (pDCF) scheme. Then the capacity of certain binary and Gaussian state-dependent orthogonal relay channels are studied in detail, and it is shown that the compress-and-forward (CF) and partial-decode-and-forward (pDF) schemes are suboptimal in general. To the best of our knowledge, this is the first single relay channel model for which the capacity is achieved by pDCF, while pDF and CF schemes are both suboptimal. Furthermore, it is shown that the capacity of the considered class of state-dependent orthogonal relay channels is in general below the cut-set bound. The conditions under which pDF or CF suffices to meet the cut-set bound, and hence, achieve the capacity, are also derived.
Managing large-scale scientific hypotheses as uncertain and probabilistic data with support for predictive analytics
Venue: arXiv cs.DB 2015
Year: 2015

The sheer scale of high-resolution raw data generated by simulation has motivated non-conventional approaches for data exploration referred as `immersive' and `in situ' query processing of the raw simulation data. Another step towards supporting scientific progress is to enable data-driven hypothesis management and predictive analytics out of simulation results. We present a synthesis method and tool for encoding and managing competing hypotheses as uncertain data in a probabilistic database that can be conditioned in the presence of observations.
Zero forcing number, constrained matchings and strong structural controllability
Venue: arXiv cs.DM 2015
Year: 2015

The zero forcing number is a graph invariant introduced to study the minimum rank of the graph. In 2008, Aazami proved the NP-hardness of computing the zero forcing number of a simple undirected graph. We complete this NP-hardness result by showing that the non-equivalent problem of computing the zero forcing number of a directed graph allowing loops is also NP-hard. The rest of the paper is devoted to the strong controllability of a networked system. This kind of controllability takes into account only the structure of the interconnection graph, but not the interconnection strengths along the edges. We provide a necessary and sufficient condition in terms of zero forcing sets for the strong controllability of a system whose underlying graph is a directed graph allowing loops. Moreover, we explain how our result differs from a recent related result discovered by Monshizadeh et al. Finally, we show how to solve the problem of finding efficiently a minimum-size input set for the strong controllability of a self-damped system with a tree-structure.
Recursive Algorithms for Distributed Forests of Octrees
Venue: arXiv cs.DC 2015
Year: 2015

The forest-of-octrees approach to parallel adaptive mesh refinement and coarsening (AMR) has recently been demonstrated in the context of a number of large-scale PDE-based applications. Although linear octrees, which store only leaf octants, have an underlying tree structure by definition, it is not often exploited in previously published mesh-related algorithms. This is because the branches are not explicitly stored, and because the topological relationships in meshes, such as the adjacency between cells, introduce dependencies that do not respect the octree hierarchy. In this work we combine hierarchical and topological relationships between octree branches to design efficient recursive algorithms. We present three important algorithms with recursive implementations. The first is a parallel search for leaves matching any of a set of multiple search criteria. The second is a ghost layer construction algorithm that handles arbitrarily refined octrees that are not covered by previous algorithms, which require a 2:1 condition between neighboring leaves. The third is a universal mesh topology iterator. This iterator visits every cell in a domain partition, as well as every interface (face, edge and corner) between these cells. The iterator calculates the local topological information for every interface that it visits, taking into account the nonconforming interfaces that increase the complexity of describing the local topology. To demonstrate the utility of the topology iterator, we use it to compute the numbering and encoding of higher-order $C^0$ nodal basis functions. We analyze the complexity of the new recursive algorithms theoretically, and assess their performance, both in terms of single-processor efficiency and in terms of parallel scalability, demonstrating good weak and strong scaling up to 458k cores of the JUQUEEN supercomputer.
The "Runs" Theorem
Venue: arXiv cs.DM 2015
Year: 2015

We give a new characterization of maximal repetitions (or runs) in strings based on Lyndon words. The characterization leads to a proof of what was known as the "runs" conjecture (Kolpakov \& Kucherov (FOCS '99)), which states that the maximum number of runs $ρ(n)$ in a string of length $n$ is less than $n$. The proof is remarkably simple, considering the numerous endeavors to tackle this problem in the last 15 years, and significantly improves our understanding of how runs can occur in strings. In addition, we obtain an upper bound of $3n$ for the maximum sum of exponents $σ(n)$ of runs in a string of length $n$, improving on the best known bound of $4.1n$ by Crochemore et al. (JDA 2012), as well as other improved bounds on related problems. The characterization also gives rise to a new, conceptually simple linear-time algorithm for computing all the runs in a string. A notable characteristic of our algorithm is that, unlike all existing linear-time algorithms, it does not utilize the Lempel-Ziv factorization of the string. We also establish a relationship between runs and nodes of the Lyndon tree, which gives a simple optimal solution to the 2-Period Query problem that was recently solved by Kociumaka et al. (SODA 2015).
Optimization for Speculative Execution of Multiple Jobs in a MapReduce-like Cluster
Venue: arXiv cs.DC 2015
Year: 2015

Nowadays, a computing cluster in a typical data center can easily consist of hundreds of thousands of commodity servers, making component/ machine failures the norm rather than exception. A parallel processing job can be delayed substantially as long as one of its many tasks is being assigned to a failing machine. To tackle this so-called straggler problem, most parallel processing frameworks such as MapReduce have adopted various strategies under which the system may speculatively launch additional copies of the same task if its progress is abnormally slow or simply because extra idling resource is available. In this paper, we focus on the design of speculative execution schemes for a parallel processing cluster under different loading conditions. For the lightly loaded case, we analyze and propose two optimization-based schemes, namely, the Smart Cloning Algorithm (SCA) which is based on maximizing the job utility and the Straggler Detection Algorithm (SDA) which minimizes the overall resource consumption of a job. We also derive the workload threshold under which SCA or SDA should be used for speculative execution. Our simulation results show both SCA and SDA can reduce the job flowtime by nearly 60% comparing to the speculative execution strategy of Microsoft Mantri. For the heavily loaded case, we propose the Enhanced Speculative Execution (ESE) algorithm which is an extension of the Microsoft Mantri scheme. We show that the ESE algorithm can beat the Mantri baseline scheme by 18% in terms of job flowtime while consuming the same amount of resource.
New Quantum Codes from Evaluation and Matrix-Product Codes
Venue: arXiv cs.IT 2015
Year: 2015

Stabilizer codes obtained via CSS code construction and Steane's enlargement of subfield-subcodes and matrix-product codes coming from generalized Reed-Muller, hyperbolic and affine variety codes are studied. Stabilizer codes with good quantum parameters are supplied, in particular, some binary codes of lengths 127 and 128 improve the parameters of the codes in http://www.codetables.de. Moreover, non-binary codes are presented either with parameters better than or equal to the quantum codes obtained from BCH codes by La Guardia or with lengths that can not be reached by them.
Parallel Algorithms for Generating Random Networks with Given Degree Sequences
Venue: arXiv cs.DC 2015
Year: 2015

Random networks are widely used for modeling and analyzing complex processes. Many mathematical models have been proposed to capture diverse real-world networks. One of the most important aspects of these models is degree distribution. Chung--Lu (CL) model is a random network model, which can produce networks with any given arbitrary degree distribution. The complex systems we deal with nowadays are growing larger and more diverse than ever. Generating random networks with any given degree distribution consisting of billions of nodes and edges or more has become a necessity, which requires efficient and parallel algorithms. We present an MPI-based distributed memory parallel algorithm for generating massive random networks using CL model, which takes $O(\frac{m+n}{P}+P)$ time with high probability and $O(n)$ space per processor, where $n$, $m$, and $P$ are the number of nodes, edges and processors, respectively. The time efficiency is achieved by using a novel load-balancing algorithm. Our algorithms scale very well to a large number of processors and can generate massive power--law networks with one billion nodes and $250$ billion edges in one minute using $1024$ processors.
Approximation Algorithms for Model-Based Compressive Sensing
Venue: arXiv cs.IT 2015
Year: 2015

Compressive Sensing (CS) stipulates that a sparse signal can be recovered from a small number of linear measurements, and that this recovery can be performed efficiently in polynomial time. The framework of model-based compressive sensing (model-CS) leverages additional structure in the signal and prescribes new recovery schemes that can reduce the number of measurements even further. However, model-CS requires an algorithm that solves the model-projection problem: given a query signal, produce the signal in the model that is also closest to the query signal. Often, this optimization can be computationally very expensive. Moreover, an approximation algorithm is not sufficient for this optimization task. As a result, the model-projection problem poses a fundamental obstacle for extending model-CS to many interesting models. In this paper, we introduce a new framework that we call approximation-tolerant model-based compressive sensing. This framework includes a range of algorithms for sparse recovery that require only approximate solutions for the model-projection problem. In essence, our work removes the aforementioned obstacle to model-based compressive sensing, thereby extending the applicability of model-CS to a much wider class of models. We instantiate this new framework for the Constrained Earth Mover Distance (CEMD) model, which is particularly useful for signal ensembles where the positions of the nonzero coefficients do not change significantly as a function of spatial (or temporal) location. We develop novel approximation algorithms for both the maximization and the minimization versions of the model-projection problem via graph optimization techniques. Leveraging these algorithms into our framework results in a nearly sample-optimal sparse recovery scheme for the CEMD model.
Reweighted Wake-Sleep
Venue: arXiv cs.LG 2015
Year: 2015

Training deep directed graphical models with many hidden variables and performing inference remains a major challenge. Helmholtz machines and deep belief networks are such models, and the wake-sleep algorithm has been proposed to train them. The wake-sleep algorithm relies on training not just the directed generative model but also a conditional generative model (the inference network) that runs backward from visible to latent, estimating the posterior distribution of latent given visible. We propose a novel interpretation of the wake-sleep algorithm which suggests that better estimators of the gradient can be obtained by sampling latent variables multiple times from the inference network. This view is based on importance sampling as an estimator of the likelihood, with the approximate inference network as a proposal distribution. This interpretation is confirmed experimentally, showing that better likelihood can be achieved with this reweighted wake-sleep procedure. Based on this interpretation, we propose that a sigmoidal belief network is not sufficiently powerful for the layers of the inference network in order to recover a good estimator of the posterior distribution of latent variables. Our experiments show that using a more powerful layer model, such as NADE, yields substantially better generative models.
Multilevel polynomial partitions and simplified range searching
Venue: arXiv cs.DS 2015
Year: 2015

The polynomial partitioning method of Guth and Katz [arXiv:1011.4105] has numerous applications in discrete and computational geometry. It partitions a given $n$-point set $P\subset\mathbb{R}^d$ using the zero set $Z(f)$ of a suitable $d$-variate polynomial $f$. Applications of this result are often complicated by the problem, what should be done with the points of $P$ lying within $Z(f)$? A natural approach is to partition these points with another polynomial and continue further in a similar manner. So far it has been pursued with limited success---several authors managed to construct and apply a second partitioning polynomial, but further progress has been prevented by technical obstacles. We provide a polynomial partitioning method with up to $d$ polynomials in dimension $d$, which allows for a complete decomposition of the given point set. We apply it to obtain a new algorithm for the semialgebraic range searching problem. Our algorithm has running time bounds similar to a recent algorithm by Agarwal, Sharir, and the first author [SIAM~J.~Comput. 42(2013) 2039--2062], but it is simpler both conceptually and technically. While this paper has been in preparation, Basu and Sombra, as well as Fox, Pach, Sheffer, Suk, and Zahl, obtained results concerning polynomial partitions which overlap with ours to some extent.
The Interplay Between Dynamics and Networks: Centrality, Communities, and Cheeger Inequality
Venue: arXiv cs.SI 2015
Year: 2015

We study the interplay between a dynamic process and the structure of the network on which it is defined. Specifically, we examine the impact of this interaction on the quality-measure of network clusters and node centrality. This enables us to effectively identify network communities and important nodes participating in the dynamics. As the first step towards this objective, we introduce an umbrella framework for defining and characterizing an ensemble of dynamic processes on a network. This framework generalizes the traditional Laplacian framework to continuous-time biased random walks and also allows us to model some epidemic processes over a network. For each dynamic process in our framework, we can define a function that measures the quality of every subset of nodes as a potential cluster (or community) with respect to this process on a given network. This subset-quality function generalizes the traditional conductance measure for graph partitioning. We partially justify our choice of the quality function by showing that the classic Cheeger's inequality, which relates the conductance of the best cluster in a network with a spectral quantity of its Laplacian matrix, can be extended from the Laplacian-conductance setting to this more general setting.
PRISM: Person Re-Identification via Structured Matching
Venue: arXiv cs.CV 2015
Year: 2015

Person re-identification (re-id), an emerging problem in visual surveillance, deals with maintaining entities of individuals whilst they traverse various locations surveilled by a camera network. From a visual perspective re-id is challenging due to significant changes in visual appearance of individuals in cameras with different pose, illumination and calibration. Globally the challenge arises from the need to maintain structurally consistent matches among all the individual entities across different camera views. We propose PRISM, a structured matching method to jointly account for these challenges. We view the global problem as a weighted graph matching problem and estimate edge weights by learning to predict them based on the co-occurrences of visual patterns in the training examples. These co-occurrence based scores in turn account for appearance changes by inferring likely and unlikely visual co-occurrences appearing in training instances. We implement PRISM on single shot and multi-shot scenarios. PRISM uniformly outperforms state-of-the-art in terms of matching rate while being computationally efficient.
On Reachability for Unidirectional Channel Systems Extended with Regular Tests
Venue: arXiv cs.LO 2015
Year: 2015

"Unidirectional channel systems" (Chambart & Schnoebelen, CONCUR 2008) are finite-state systems where one-way communication from a Sender to a Receiver goes via one reliable and one unreliable unbounded fifo channel. While reachability is decidable for these systems, equipping them with the possibility of testing regular properties on the contents of channels makes it undecidable. Decidability is preserved when only emptiness and nonemptiness tests are considered: the proof relies on an elaborate reduction to a generalized version of Post's Embedding Problem.
Optimal Offline Packet Scheduling in Energy Harvesting 2-user Multiple Access Channel with Common Data
Venue: arXiv cs.IT 2015
Year: 2015

The lifetime and the sustainability of the wireless sensor networks (WSNs) can be increased with energy harvesting transmitters utilizing optimum packet scheduling. On the other hand, WSNs are observed to collect spatially or temporally correlated data which should be taken into account for the optimum packet scheduling in an energy harvesting system. However, the solutions available for 2-user multiple-access channel (MAC) systems with energy harvesting transmitters do not consider the common data or the correlation among the data. In this paper, optimal packet scheduling for energy harvesting 2-user Gaussian MAC with common data is achieved by assuming deterministic knowledge of the data and energy packets, i.e., offline solution. The optimum departure region is found by using Karush- Kuhn-Tucker (KKT) conditions generalizing the solutions obtained for the MAC without common data. An efficient iterative backward water-filling algorithm is defined. The optimum solution is numerically compared with the case of no scheduling, uniform power scheduling and the previous solutions defined for the MAC without common data by showing the improvement obtained with the optimization.