OpenRaiser/Intern-Atlas huggingface dataset:
Improved Space efficient linear time algorithms for BFS, DFS and applications
Venue: arXiv cs.DS 2017
Year: 2017

Recent work by Elmasry et al. (STACS 2015) and Asano et al. (ISAAC 2014), reconsidered classical fundamental graph algorithms focusing on improving the space complexity. We continue this line of work focusing on space. Our first result is a simple data structure that can maintain any subset $S$ of a universe of $n$ elements using $n+o(n)$ bits and support in constant time, apart from the standard insert, delete and membership queries, the operation {\it findany} that finds and returns any element of the set (or outputs that the set is empty). Using this we give a BFS implementation that takes $O(m+n)$ time using at most $2n+o(n)$ bits. Later, we further improve the space requirement of BFS to at most $1.585n + o(n)$ bits. We demonstrate the use of our data structure by developing another data structure using it that can represent a sequence of $n$ non-negative integers $x_1, x_2, \ldots x_n$ using at most $\sum_{i=1}^n x_i + 2n + o(\sum_{i=1}^n x_i+n)$ bits and, in constant time, determine whether the $i$-th element is $0$ or decrement it otherwise. We also discuss an algorithm for finding a minimum weight spanning tree of a weighted undirected graph using at most $n+o(n)$ bits. We also provide an implementation for DFS that takes $O(m+n)$ time and $O(n \lg(m/n))$ bits. Using this DFS algorithm and other careful implementations, we can test biconnectivity, 2-edge connectivity, and determine cut vertices, bridges etc among others, essentially within the same time and space bounds required for DFS. These improve the space required for earlier implementations from $Ω(n\lg n)$ bits.
Reciprocity Calibration for Massive MIMO: Proposal, Modeling and Validation
Venue: arXiv cs.IT 2017
Year: 2017

This paper presents a mutual coupling based calibration method for time-division-duplex massive MIMO systems, which enables downlink precoding based on uplink channel estimates. The entire calibration procedure is carried out solely at the base station (BS) side by sounding all BS antenna pairs. An Expectation-Maximization (EM) algorithm is derived, which processes the measured channels in order to estimate calibration coefficients. The EM algorithm outperforms current state-of-the-art narrow-band calibration schemes in a mean squared error (MSE) and sum-rate capacity sense. Like its predecessors, the EM algorithm is general in the sense that it is not only suitable to calibrate a co-located massive MIMO BS, but also very suitable for calibrating multiple BSs in distributed MIMO systems. The proposed method is validated with experimental evidence obtained from a massive MIMO testbed. In addition, we address the estimated narrow-band calibration coefficients as a stochastic process across frequency, and study the subspace of this process based on measurement data. With the insights of this study, we propose an estimator which exploits the structure of the process in order to reduce the calibration error across frequency. A model for the calibration error is also proposed based on the asymptotic properties of the estimator, and is validated with measurement results.
Weighted Online Problems with Advice
Venue: arXiv cs.DS 2017
Year: 2017

Recently, the first online complexity class, AOC, was introduced. The class consists of many online problems where each request must be either accepted or rejected, and the aim is to either minimize or maximize the number of accepted requests, while maintaining a feasible solution. All AOC-complete problems (including Independent Set, Vertex Cover, Dominating Set, and Set Cover) have essentially the same advice complexity. In this paper, we study weighted versions of problems in AOC, i.e., each request comes with a weight and the aim is to either minimize or maximize the total weight of the accepted requests. In contrast to the unweighted versions, we show that there is a significant difference in the advice complexity of complete minimization and maximization problems. We also show that our algorithmic techniques for dealing with weighted requests can be extended to work for non-complete AOC problems such as maximum matching (giving better results than what follow from the general AOC results) and even non-AOC problems such as scheduling.
Mobility-Aware Caching in D2D Networks
Venue: arXiv cs.IT 2017
Year: 2017

Caching at mobile devices can facilitate device-to-device (D2D) communications, which may significantly improve spectrum efficiency and alleviate the heavy burden on backhaul links. However, most previous works ignored user mobility, thus having limited practical applications. In this paper, we take advantage of the user mobility pattern by the inter-contact times between different users, and propose a mobility-aware caching placement strategy to maximize the data offloading ratio, which is defined as the percentage of the requested data that can be delivered via D2D links rather than through base stations (BSs). Given the NP-hard caching placement problem, we first propose an optimal dynamic programming (DP) algorithm to obtain a performance benchmark, but with much lower complexity than exhaustive search. We will then prove that the problem falls in the category of monotone submodular maximization over a matroid constraint, and propose a time-efficient greedy algorithm, which achieves an approximation ratio as 1/2. Simulation results with real-life data-sets will validate the effectiveness of our proposed mobility-aware caching placement strategy. We observe that users moving at either a very low or very high speed should cache the most popular files, while users moving at a medium speed should cache less popular files to avoid duplication.
Metastability-Containing Circuits
Venue: arXiv cs.DC 2017
Year: 2017

In digital circuits, metastability can cause deteriorated signals that neither are logical 0 or logical 1, breaking the abstraction of Boolean logic. Unfortunately, any way of reading a signal from an unsynchronized clock domain or performing an analog-to-digital conversion incurs the risk of a metastable upset; no digital circuit can deterministically avoid, resolve, or detect metastability (Marino, 1981). Synchronizers, the only traditional countermeasure, exponentially decrease the odds of maintained metastability over time. Trading synchronization delay for an increased probability to resolve metastability to logical 0 or 1, they do not guarantee success. We propose a fundamentally different approach: It is possible to contain metastability by fine-grained logical masking so that it cannot infect the entire circuit. This technique guarantees a limited degree of metastability in---and uncertainty about---the output. At the heart of our approach lies a time- and value-discrete model for metastability in synchronous clocked digital circuits. Metastability is propagated in a worst-case fashion, allowing to derive deterministic guarantees, without and unlike synchronizers. The proposed model permits positive results and passes the test of reproducing Marino's impossibility results. We fully classify which functions can be computed by circuits with standard registers. Regarding masking registers, we show that they become computationally strictly more powerful with each clock cycle, resulting in a non-trivial hierarchy of computable functions.
A Self-Index on Block Trees
Venue: arXiv cs.DS 2017
Year: 2017

The Block Tree is a recently proposed data structure that reaches compression close to Lempel-Ziv while supporting efficient direct access to text substrings. In this paper we show how a self-index can be built on top of a Block Tree so that it provides efficient pattern searches while using space proportional to that of the original data structure. More precisely, if a Lempel-Ziv parse cuts a text of length $n$ into $z$ non-overlapping phrases, then our index uses $O(z\log(n/z))$ words and finds the $occ$ occurrences of a pattern of length $m$ in time $O(m\log n+occ\log^εn)$ for any constant $ε>0$.
Optimal Thresholds for Anomaly-Based Intrusion Detection in Dynamical Environments
Venue: arXiv cs.GT 2017
Year: 2017

In cyber-physical systems, malicious and resourceful attackers could penetrate the system through cyber means and cause significant physical damage. Consequently, detection of such attacks becomes integral towards making these systems resilient to attacks. To achieve this objective, intrusion detection systems (IDS) that are able to detect malicious behavior can be deployed. However, practical IDS are imperfect and sometimes they may produce false alarms for a normal system behavior. Since alarms need to be investigated for any potential damage, a large number of false alarms may increase the operational costs significantly. Thus, IDS need to be configured properly, as oversensitive IDS could detect attacks early but at the cost of a higher number of false alarms. Similarly, IDS with low sensitivity could reduce the false alarms while increasing the time to detect the attacks. The configuration of IDS to strike the right balance between time to detecting attacks and the rate of false positives is a challenging task, especially in dynamic environments, in which the damage incurred by a successful attack is time-varying. In this paper, we study the problem of finding optimal detection thresholds for anomaly-based detectors implemented in dynamical systems in the face of strategic attacks. We formulate the problem as an attacker-defender security game, and determine thresholds for the detector to achieve an optimal trade-off between the detection delay and the false positive rates. In this direction, first, we provide an algorithm that computes optimal fixed threshold that remains fixed throughout. Second, we allow detector's threshold to change with time to further minimize the defender's loss and provide an algorithm to compute time-varying thresholds, which we call adaptive thresholds. Finally, we numerically evaluate our results using a water distribution network as a case-study.
Ancestral Causal Inference
Venue: arXiv cs.LG 2017
Year: 2017

Constraint-based causal discovery from limited data is a notoriously difficult challenge due to the many borderline independence test decisions. Several approaches to improve the reliability of the predictions by exploiting redundancy in the independence information have been proposed recently. Though promising, existing approaches can still be greatly improved in terms of accuracy and scalability. We present a novel method that reduces the combinatorial explosion of the search space by using a more coarse-grained representation of causal information, drastically reducing computation time. Additionally, we propose a method to score causal predictions based on their confidence. Crucially, our implementation also allows one to easily combine observational and interventional data and to incorporate various types of available background knowledge. We prove soundness and asymptotic consistency of our method and demonstrate that it can outperform the state-of-the-art on synthetic data, achieving a speedup of several orders of magnitude. We illustrate its practical feasibility by applying it on a challenging protein data set.
Learning to Poke by Poking: Experiential Learning of Intuitive Physics
Venue: arXiv cs.CV 2017
Year: 2017

We investigate an experiential learning paradigm for acquiring an internal model of intuitive physics. Our model is evaluated on a real-world robotic manipulation task that requires displacing objects to target locations by poking. The robot gathered over 400 hours of experience by executing more than 100K pokes on different objects. We propose a novel approach based on deep neural networks for modeling the dynamics of robot's interactions directly from images, by jointly estimating forward and inverse models of dynamics. The inverse model objective provides supervision to construct informative visual features, which the forward model can then predict and in turn regularize the feature space for the inverse model. The interplay between these two objectives creates useful, accurate models that can then be used for multi-step decision making. This formulation has the additional benefit that it is possible to learn forward models in an abstract feature space and thus alleviate the need of predicting pixels. Our experiments show that this joint modeling approach outperforms alternative methods.
Enriching Linked Datasets with New Object Properties
Venue: arXiv cs.DB 2017
Year: 2017

Although several RDF knowledge bases are available through the LOD initiative, the ontology schema of such linked datasets is not very rich. In particular, they lack object properties. The problem of finding new object properties (and their instances) between any two given classes has not been investigated in detail in the context of Linked Data. In this paper, we present DART (Detecting Arbitrary Relations for enriching T-Boxes of Linked Data) - an unsupervised solution to enrich the LOD cloud with new object properties between two given classes. DART exploits contextual similarity to identify text patterns from the web corpus that can potentially represent relations between individuals. These text patterns are then clustered by means of paraphrase detection to capture the object properties between the two given LOD classes. DART also performs fully automated mapping of the discovered relations to the properties in the linked dataset. This serves many purposes such as identification of completely new relations, elimination of irrelevant relations, and generation of prospective property axioms. We have empirically evaluated our approach on several pairs of classes and found that the system can indeed be used for enriching the linked datasets with new object properties and their instances. We compared DART with newOntExt system which is an offshoot of the NELL (Never-Ending Language Learning) effort. Our experiments reveal that DART gives better results than newOntExt with respect to both the correctness, as well as the number of relations.
Optimal redundancy in computations from random oracles
Venue: arXiv cs.CC 2017
Year: 2017

A classic result in algorithmic information theory is that every infinite binary sequence is computable from a Martin-Loef random infinite binary sequence. Proved independently by Kucera and Gacs, this result answered a question by Charles Bennett and has seen numerous applications in the last 30 years. The optimal redundancy in such a coding process has, however, remained unknown. If the computation of the first n bits of a sequence requires n + g(n) bits of the random oracle, then g is the redundancy of the computation. Kucera implicitly achieved redundancy n log n while Gacs used a more elaborate block-coding procedure which achieved redundancy sqrt(n) log n. Different approaches to coding such as the one by Merkle and Mihailovic have not improved this redundancy bound. In this paper we devise a new coding method that achieves optimal logarithmic redundancy. Our redundancy bound is exponentially smaller than the previously best known bound and is known to be the best possible. It follows that redundancy r log n in computation from a random oracle is possible for every stream, if and only if r > 1.
Sampling and Reconstruction of Sparse Signals on Circulant Graphs - An Introduction to Graph-FRI
Venue: arXiv cs.DM 2017
Year: 2017

With the objective of employing graphs toward a more generalized theory of signal processing, we present a novel sampling framework for (wavelet-)sparse signals defined on circulant graphs which extends basic properties of Finite Rate of Innovation (FRI) theory to the graph domain, and can be applied to arbitrary graphs via suitable approximation schemes. At its core, the introduced Graph-FRI-framework states that any K-sparse signal on the vertices of a circulant graph can be perfectly reconstructed from its dimensionality-reduced representation in the graph spectral domain, the Graph Fourier Transform (GFT), of minimum size 2K. By leveraging the recently developed theory of e-splines and e-spline wavelets on graphs, one can decompose this graph spectral transformation into the multiresolution low-pass filtering operation with a graph e-spline filter, and subsequent transformation to the spectral graph domain; this allows to infer a distinct sampling pattern, and, ultimately, the structure of an associated coarsened graph, which preserves essential properties of the original, including circularity and, where applicable, the graph generating set.
A width parameter useful for chordal and co-comparability graphs
Venue: arXiv cs.DS 2017
Year: 2017

We investigate new graph classes of bounded mim-width, strictly extending interval graphs and permutation graphs. The graphs $K_t \boxminus K_t$ and $K_t \boxminus S_t$ are graphs obtained from the disjoint union of two cliques of size $t$, and one clique of size $t$ and one independent set of size $t$ respectively, by adding a perfect matching. We prove that : (1) interval graphs are $(K_3\boxminus S_3)$-free chordal graphs; and $(K_t\boxminus S_t)$-free chordal graphs have mim-width at most $t-1$, (2) permutation graphs are $(K_3\boxminus K_3)$-free co-comparability graphs; and $(K_t\boxminus K_t)$-free co-comparability graphs have mim-width at most $t-1$, (3) chordal graphs and co-comparability graphs have unbounded mim-width in general. We obtain several algorithmic consequences; for instance, while Minimum Dominating Set is NP-complete on chordal graphs, it can be solved in time $n^{\mathcal{O}(t)}$ on $(K_t\boxminus S_t)$-free chordal graphs. The third statement strengthens a result of Belmonte and Vatshelle stating that either those classes do not have constant mim-width or a decomposition with constant mim-width cannot be computed in polynomial time unless $P=NP$. We generalize these ideas to bigger graph classes. We introduce a new width parameter sim-width, of stronger modelling power than mim-width, by making a small change in the definition of mim-width. We prove that chordal graphs and co-comparability graphs have sim-width at most 1. We investigate a way to bound mim-width for graphs of bounded sim-width by excluding $K_t\boxminus K_t$ and $K_t\boxminus S_t$ as induced minors or induced subgraphs, and give algorithmic consequences. Lastly, we show that circle graphs have unbounded sim-width, and thus also unbounded mim-width.
A Class of Diffusion Algorithms with Logarithmic Cost over Adaptive Sparse Volterra Network
Venue: arXiv cs.SY 2017
Year: 2017

In this Letter, we present a novel class of diffusion algorithms that can be used to estimate the coefficients of sparse Volterra network (SVN). The development of the algorithms is based on the logarithmic cost and l0-norm constraint. Simulations for Gaussian and impulsive scenarios are conducted to demonstrate the superior performance of the proposed algorithms as compared with the existing algorithms.
Exact Lower Bounds for the Agnostic Probably-Approximately-Correct (PAC) Machine Learning Model
Venue: arXiv cs.LG 2017
Year: 2017

We provide an exact non-asymptotic lower bound on the minimax expected excess risk (EER) in the agnostic probably-ap\-proximately-correct (PAC) machine learning classification model and identify minimax learning algorithms as certain maximally symmetric and minimally randomized "voting" procedures. Based on this result, an exact asymptotic lower bound on the minimax EER is provided. This bound is of the simple form $c_\infty/\sqrtν$ as $ν\to\infty$, where $c_\infty=0.16997\dots$ is a universal constant, $ν=m/d$, $m$ is the size of the training sample, and $d$ is the Vapnik--Chervonenkis dimension of the hypothesis class. It is shown that the differences between these asymptotic and non-asymptotic bounds, as well as the differences between these two bounds and the maximum EER of any learning algorithms that minimize the empirical risk, are asymptotically negligible, and all these differences are due to ties in the mentioned "voting" procedures. A few easy to compute non-asymptotic lower bounds on the minimax EER are also obtained, which are shown to be close to the exact asymptotic lower bound $c_\infty/\sqrtν$ even for rather small values of the ratio $ν=m/d$. As an application of these results, we substantially improve existing lower bounds on the tail probability of the excess risk. Among the tools used are Bayes estimation and apparently new identities and inequalities for binomial distributions.
Proof Diagrams for Multiplicative Linear Logic
Venue: arXiv cs.LO 2017
Year: 2017

The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof in sequent calculus. In this paper we give an interpretation of proof nets in the syntax of string diagrams. Even though we lose standard proof equivalence, our construction allows to define a framework where soundness and well-typeness of a diagram can be verified in linear time.
Algebraic foundations for qualitative calculi and networks
Venue: arXiv cs.AI 2017
Year: 2017

A qualitative representation $ϕ$ is like an ordinary representation of a relation algebra, but instead of requiring $(a; b)^ϕ= a^ϕ| b^ϕ$, as we do for ordinary representations, we only require that $c^ϕ\supseteq a^ϕ| b^ϕ\iff c\geq a ; b$, for each $c$ in the algebra. A constraint network is qualitatively satisfiable if its nodes can be mapped to elements of a qualitative representation, preserving the constraints. If a constraint network is satisfiable then it is clearly qualitatively satisfiable, but the converse can fail. However, for a wide range of relation algebras including the point algebra, the Allen Interval Algebra, RCC8 and many others, a network is satisfiable if and only if it is qualitatively satisfiable. Unlike ordinary composition, the weak composition arising from qualitative representations need not be associative, so we can generalise by considering network satisfaction problems over non-associative algebras. We prove that computationally, qualitative representations have many advantages over ordinary representations: whereas many finite relation algebras have only infinite representations, every finite qualitatively representable algebra has a finite qualitative representation; the representability problem for (the atom structures of) finite non-associative algebras is NP-complete; the network satisfaction problem over a finite qualitatively representable algebra is always in NP; the validity of equations over qualitative representations is co-NP-complete. On the other hand we prove that there is no finite axiomatisation of the class of qualitatively representable algebras.
Proximity Operators of Discrete Information Divergences
Venue: arXiv cs.IT 2017
Year: 2017

Information divergences allow one to assess how close two distributions are from each other. Among the large panel of available measures, a special attention has been paid to convex $φ$-divergences, such as Kullback-Leibler, Jeffreys-Kullback, Hellinger, Chi-Square, Renyi, and I$_α$ divergences. While $φ$-divergences have been extensively studied in convex analysis, their use in optimization problems often remains challenging. In this regard, one of the main shortcomings of existing methods is that the minimization of $φ$-divergences is usually performed with respect to one of their arguments, possibly within alternating optimization techniques. In this paper, we overcome this limitation by deriving new closed-form expressions for the proximity operator of such two-variable functions. This makes it possible to employ standard proximal methods for efficiently solving a wide range of convex optimization problems involving $φ$-divergences. In addition, we show that these proximity operators are useful to compute the epigraphical projection of several functions of practical interest. The proposed proximal tools are numerically validated in the context of optimal query execution within database management systems, where the problem of selectivity estimation plays a central role. Experiments are carried out on small to large scale scenarios.