OpenRaiser/Intern-Atlas huggingface dataset:
Non-Orthogonal Tensor Diagonalization
Venue: arXiv cs.NA 2016
Year: 2016

Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices along selected dimensions of the tensor. It is generalization of approximate joint diagonalization (AJD) of a set of matrices. In particular, we derive (1) a new algorithm for symmetric AJD, which is called two-sided symmetric diagonalization of order-three tensor, (2) a similar algorithm for non-symmetric AJD, also called general two-sided diagonalization of an order-3 tensor, and (3) an algorithm for three-sided diagonalization of order-3 or order-4 tensors. The latter two algorithms may serve for canonical polyadic (CP) tensor decomposition, and they can outperform other CP tensor decomposition methods in terms of computational speed under the restriction that the tensor rank does not exceed the tensor multilinear rank. Finally, we propose (4) similar algorithms for tensor block diagonalization, which is related to the tensor block-term decomposition.
TrendLearner: Early Prediction of Popularity Trends of User Generated Content
Venue: arXiv cs.SI 2016
Year: 2016

We here focus on the problem of predicting the popularity trend of user generated content (UGC) as early as possible. Taking YouTube videos as case study, we propose a novel two-step learning approach that: (1) extracts popularity trends from previously uploaded objects, and (2) predicts trends for new content. Unlike previous work, our solution explicitly addresses the inherent tradeoff between prediction accuracy and remaining interest in the content after prediction, solving it on a per-object basis. Our experimental results show great improvements of our solution over alternatives, and its applicability to improve the accuracy of state-of-the-art popularity prediction methods.
Secure Equilibria in Weighted Games
Venue: arXiv cs.GT 2016
Year: 2016

We consider two-player non zero-sum infinite duration games played on weighted graphs. We extend the notion of secure equilibrium introduced by Chatterjee et al., from the Boolean setting to this quantitative setting. As for the Boolean setting, our notion of secure equilibrium refines the classical notion of Nash equilibrium. We prove that secure equilibria always exist in a large class of weighted games which includes common measures like sup, inf, lim sup, lim inf, mean-payoff, and discounted sum. Moreover we show that one can synthesize finite-memory strategy profiles with few memory. We also prove that the constrained existence problem for secure equilibria is decidable for sup, inf, lim sup, lim inf and mean-payoff measures. Our solutions rely on new results for zero-sum quantitative games with lexicographic objectives that are interesting on their own right.
Finding Preference Profiles of Condorcet Dimension $k$ via SAT
Venue: arXiv cs.MA 2016
Year: 2016

Condorcet winning sets are a set-valued generalization of the well-known concept of a Condorcet winner. As supersets of Condorcet winning sets are always Condorcet winning sets themselves, an interesting property of preference profiles is the size of the smallest Condorcet winning set they admit. This smallest size is called the Condorcet dimension of a preference profile. Since little is known about profiles that have a certain Condorcet dimension, we show in this paper how the problem of finding a preference profile that has a given Condorcet dimension can be encoded as a satisfiability problem and solved by a SAT solver. Initial results include a minimal example of a preference profile of Condorcet dimension 3, improving previously known examples both in terms of the number of agents as well as alternatives. Due to the high complexity of such problems it remains open whether a preference profile of Condorcet dimension 4 exists.
Turing Kernelization for Finding Long Paths and Cycles in Restricted Graph Classes
Venue: arXiv cs.DS 2016
Year: 2016

The NP-complete $k$-Path problem asks whether a given undirected graph has a (simple) path of length at least $k$. We prove that $k$-Path has polynomial-size Turing kernels when restricted to planar graphs, graphs of bounded degree, claw-free graphs, or to $K_{3,t}$-minor-free graphs for some constant $t$. This means that there is an algorithm that, given a $k$-Path instance $(G,k)$ belonging to one of these graph classes, computes its answer in polynomial time when given access to an oracle that solves $k$-Path instances of size polynomial in $k$ in a single step. The difficulty of $k$-Path can therefore be confined to subinstances whose size is independent of the total input size, but is bounded by a polynomial in the parameter $k$ alone. These results contrast existing superpolynomial lower bounds for the sizes of traditional kernels for the $k$-Path problem on these graph classes: there is no polynomial-time algorithm that reduces any instance $(G,k)$ to a single, equivalent instance $(G',k')$ of size polynomial in $k$ unless $NP \subseteq coNP/poly$. The same positive and negative results apply to the $k$-Cycle problem, which asks for the existence of a cycle of length at least $k$. Our kernelization schemes are based on a new methodology called Decompose-Query-Reduce.
Shifting coresets: obtaining linear-time approximations for unit disk graphs and other geometric intersection graphs
Venue: arXiv cs.DS 2016
Year: 2016

Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy that allows us to obtain linear-time constant-factor approximation algorithms for such problems. To illustrate the applicability of the proposed variation, we obtain results for three well-known optimization problems. Among such results, the proposed method yields linear-time (4+eps)-approximation for the maximum-weight independent set and the minimum dominating set of unit disk graphs, thus bringing significant performance improvements when compared to previous algorithms that achieve the same approximation ratios. Finally, we use axis-aligned rectangles to illustrate that the same method may be used to derive linear-time approximations for problems on other geometric intersection graph classes.
An experimental exploration of Marsaglia's xorshift generators, scrambled
Venue: arXiv cs.DS 2016
Year: 2016

Marsaglia proposed recently xorshift generators as a class of very fast, good-quality pseudorandom number generators. Subsequent analysis by Panneton and L'Ecuyer has lowered the expectations raised by Marsaglia's paper, showing several weaknesses of such generators, verified experimentally using the TestU01 suite. Nonetheless, many of the weaknesses of xorshift generators fade away if their result is scrambled by a non-linear operation (as originally suggested by Marsaglia). In this paper we explore the space of possible generators obtained by multiplying the result of a xorshift generator by a suitable constant. We sample generators at 100 equispaced points of their state space and obtain detailed statistics that lead us to choices of parameters that improve on the current ones. We then explore for the first time the space of high-dimensional xorshift generators, following another suggestion in Marsaglia's paper, finding choices of parameters providing periods of length $2^{1024} - 1$ and $2^{4096} - 1$. The resulting generators are of extremely high quality, faster than current similar alternatives, and generate long-period sequences passing strong statistical tests using only eight logical operations, one addition and one multiplication by a constant.
Better bitmap performance with Roaring bitmaps
Venue: arXiv cs.DB 2016
Year: 2016

Bitmap indexes are commonly used in databases and search engines. By exploiting bit-level parallelism, they can significantly accelerate queries. However, they can use much memory, and thus we might prefer compressed bitmap indexes. Following Oracle's lead, bitmaps are often compressed using run-length encoding (RLE). Building on prior work, we introduce the Roaring compressed bitmap format: it uses packed arrays for compression instead of RLE. We compare it to two high-performance RLE-based bitmap encoding techniques: WAH (Word Aligned Hybrid compression scheme) and Concise (Compressed `n' Composable Integer Set). On synthetic and real data, we find that Roaring bitmaps (1) often compress significantly better (e.g., 2 times) and (2) are faster than the compressed alternatives (up to 900 times faster for intersections). Our results challenge the view that RLE-based bitmap compression is best.
Categorization Axioms for Clustering Results
Venue: arXiv cs.LG 2016
Year: 2016

Cluster analysis has attracted more and more attention in the field of machine learning and data mining. Numerous clustering algorithms have been proposed and are being developed due to diverse theories and various requirements of emerging applications. Therefore, it is very worth establishing an unified axiomatic framework for data clustering. In the literature, it is an open problem and has been proved very challenging. In this paper, clustering results are axiomatized by assuming that an proper clustering result should satisfy categorization axioms. The proposed axioms not only introduce classification of clustering results and inequalities of clustering results, but also are consistent with prototype theory and exemplar theory of categorization models in cognitive science. Moreover, the proposed axioms lead to three principles of designing clustering algorithm and cluster validity index, which follow many popular clustering algorithms and cluster validity indices.
Joint Power Control in Wiretap Interference Channels
Venue: arXiv cs.IT 2016
Year: 2016

Interference in wireless networks degrades the signal quality at the terminals. However, it can potentially enhance the secrecy rate. This paper investigates the secrecy rate in a two-user interference network where one of the users, namely user 1, requires to establish a confidential connection. User 1 wants to prevent an unintended user of the network to decode its transmission. User 1 has to transmit such that its secrecy rate is maximized while the quality of service at the destination of the other user, user 2, is satisfied, and both user's power limits are taken into account. We consider two scenarios: 1) user 2 changes its power in favor of user 1, an altruistic scenario, 2) user 2 is selfish and only aims to maintain the minimum quality of service at its destination, an egoistic scenario. It is shown that there is a threshold for user 2's transmission power that only below or above which, depending on the channel qualities, user 1 can achieve a positive secrecy rate. Closed-form solutions are obtained in order to perform joint optimal power control. Further, a new metric called secrecy energy efficiency is introduced. We show that in general, the secrecy energy efficiency of user 1 in an interference channel scenario is higher than that of an interference-free channel.
Subset Synchronization and Careful Synchronization of Binary Finite Automata
Venue: arXiv cs.FL 2016
Year: 2016

We present a strongly exponential lower bound that applies both to the subset synchronization threshold for binary deterministic automata and to the careful synchronization threshold for binary partial automata. In the later form, the result finishes the research initiated by Martyugin (2013). Moreover, we show that both the thresholds remain strongly exponential even if restricted to strongly connected binary automata. In addition, we apply our methods to computational complexity. Existence of a subset reset word is known to be PSPACE-complete; we show that this holds even under the restriction to strongly connected binary automata. The results apply also to the corresponding thresholds in two more general settings: D1- and D3-directable nondeterministic automata and composition sequences over finite domains.
On weak differential uniformity of vectorial Boolean functions as a cryptographic criterion
Venue: arXiv cs.CR 2016
Year: 2016

We study the relation among some security parameters for vectorial Boolean functions which prevent attacks on the related block cipher. We focus our study on a recently-introduced security criterion, called weak differential uniformity, which prevents the existence of an undetectable trapdoor based on imprimitive group action. We present some properties of functions with low weak differential uniformity, especially for the case of power functions and 4-bit S-Boxes.
Posterior Matching for Gaussian Broadcast Channels with Feedback
Venue: arXiv cs.IT 2016
Year: 2016

In this paper, the posterior matching scheme proposed by Shayevits and Feder is extended to the Gaussian broadcast channel with feedback, and the error probabilities and achievable rate region are derived for this coding strategy by using the iterated random function theory. A variant of the Ozarow-Leung code for the general two-user broadcast channel with feedback can be realized as a special case of our coding scheme. Furthermore, for the symmetric Gaussian broadcast channel with feedback, our coding scheme achieves the linear-feedback sum-capacity like the LQG code and outperforms the Kramer code.
Further Hardness Results on Rainbow and Strong Rainbow Connectivity
Venue: arXiv cs.CC 2016
Year: 2016

A path in an edge-colored graph is \textit{rainbow} if no two edges of it are colored the same. The graph is said to be \textit{rainbow connected} if there is a rainbow path between every pair of vertices. If there is a rainbow shortest path between every pair of vertices, the graph is \textit{strong rainbow connected}. We consider the complexity of the problem of deciding if a given edge-colored graph is rainbow or strong rainbow connected. These problems are called \textsc{Rainbow connectivity} and \textsc{Strong rainbow connectivity}, respectively. We prove both problems remain $\NP$\hyp{}complete on interval outerplanar graphs and $k$-regular graphs for $k \geq 3$. Previously, no graph class was known where the complexity of the two problems would differ. We show that for block graphs, which form a subclass of chordal graphs, \textsc{Rainbow connectivity} is $\NP$\hyp{}complete while \textsc{Strong rainbow connectivity} is in $¶$. We conclude by considering some tractable special cases, and show for instance that both problems are in $\XP$ when parameterized by tree-depth.
Modeling the wind circulation around mills with a Lagrangian stochastic approach
Venue: arXiv cs.CE 2016
Year: 2016

This work aims at introducing model methodology and numerical studies related to a Lagrangian stochastic approach applied to the computation of the wind circulation around mills. We adapt the Lagrangian stochastic downscaling method that we have introduced in [3] and [4] to the atmospheric boundary layer and we introduce here a Lagrangian version of the actuator disc methods to take account of the mills. We present our numerical method and numerical experiments in the case of non rotating and rotating actuator disc models. We also present some features of our numerical method, in particular the computation of the probability distribution of the wind in the wake zone, as a byproduct of the fluid particle model and the associated PDF method.
A heuristic prover for real inequalities
Venue: arXiv cs.MS 2016
Year: 2016

We describe a general method for verifying inequalities between real-valued expressions, especially the kinds of straightforward inferences that arise in interactive theorem proving. In contrast to approaches that aim to be complete with respect to a particular language or class of formulas, our method establishes claims that require heterogeneous forms of reasoning, relying on a Nelson-Oppen-style architecture in which special-purpose modules collaborate and share information. The framework is thus modular and extensible. A prototype implementation shows that the method works well on a variety of examples, and complements techniques that are used by contemporary interactive provers.
Secure Degrees of Freedom of the MIMO Multiple Access Channel with Multiple unknown Eavesdroppers
Venue: arXiv cs.IT 2016
Year: 2016

We investigate the secure degrees of freedom (SDoF) of a two-transmitter Gaussian multiple access channel with multiple antennas at the transmitters, the legitimate receiver with the existence of an unknown number of eavesdroppers each with a number of antennas less than or equal to a known value $N_E$. The channel matrices between the legitimate transmitters and the receiver are available everywhere, while the legitimate pair does not know the eavesdroppers' channels matrices. We provide the exact sum SDoF for the considered system. A new comprehensive upperbound is deduced and a new achievable scheme based on utilizing jamming is exploited. We prove that Cooperative Jamming is SDoF optimal even without the instantaneous eavesdropper CSI available at the transmitters.
Win-Win Kernelization for Degree Sequence Completion Problems
Venue: arXiv cs.DM 2016
Year: 2016

We study provably effective and efficient data reduction for a class of NP-hard graph modification problems based on vertex degree properties. We show fixed-parameter tractability for NP-hard graph completion (that is, edge addition) cases while we show that there is no hope to achieve analogous results for the corresponding vertex or edge deletion versions. Our algorithms are based on transforming graph completion problems into efficiently solvable number problems and exploiting f-factor computations for translating the results back into the graph setting. Our core observation is that we encounter a win-win situation: either the number of edge additions is small or the problem is polynomial-time solvable. This approach helps in answering an open question by Mathieson and Szeider [JCSS 2012] concerning the polynomial kernelizability of Degree Constraint Edge Addition and leads to a general method of approaching polynomial-time preprocessing for a wider class of degree sequence completion problems.
Identification, location-domination and metric dimension on interval and permutation graphs. II. Algorithms and complexity
Venue: arXiv cs.DM 2016
Year: 2016

We consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets (denoted IDENTIFYING CODE, (OPEN) LOCATING-DOMINATING SET and METRIC DIMENSION) of an interval or a permutation graph. In these problems, one asks to distinguish all vertices of a graph by a subset of the vertices, using either the neighbourhood within the solution set or the distances to the solution vertices. Using a general reduction for this class of problems, we prove that the decision problems associated to these four notions are NP-complete, even for interval graphs of diameter $2$ and permutation graphs of diameter $2$. While IDENTIFYING CODE and (OPEN) LOCATING-DOMINATING SET are trivially fixed-parameter-tractable when parameterized by solution size, it is known that in the same setting METRIC DIMENSION is $W[2]$-hard. We show that for interval graphs, this parameterization of METRIC DIMENSION is fixed-parameter-tractable.
Active network management for electrical distribution systems: problem formulation, benchmark, and approximate solution
Venue: arXiv cs.SY 2016
Year: 2016

With the increasing share of renewable and distributed generation in electrical distribution systems, Active Network Management (ANM) becomes a valuable option for a distribution system operator to operate his system in a secure and cost-effective way without relying solely on network reinforcement. ANM strategies are short-term policies that control the power injected by generators and/or taken off by loads in order to avoid congestion or voltage issues. Advanced ANM strategies imply that the system operator has to solve large-scale optimal sequential decision-making problems under uncertainty. For example, decisions taken at a given moment constrain the future decisions that can be taken and uncertainty must be explicitly accounted for because neither demand nor generation can be accurately forecasted. We first formulate the ANM problem, which in addition to be sequential and uncertain, has a nonlinear nature stemming from the power flow equations and a discrete nature arising from the activation of power modulation signals. This ANM problem is then cast as a stochastic mixed-integer nonlinear program, as well as second-order cone and linear counterparts, for which we provide quantitative results using state of the art solvers and perform a sensitivity analysis over the size of the system, the amount of available flexibility, and the number of scenarios considered in the deterministic equivalent of the stochastic program. To foster further research on this problem, we make available at http://www.montefiore.ulg.ac.be/~anm/ three test beds based on distribution networks of 5, 33, and 77 buses. These test beds contain a simulator of the distribution system, with stochastic models for the generation and consumption devices, and callbacks to implement and test various ANM strategies.
Language to Specify Syntax-Guided Synthesis Problems
Venue: arXiv cs.PL 2016
Year: 2016

We present a language to specify syntax guided synthesis (SyGuS) problems. Syntax guidance is a prominent theme in contemporary program synthesis approaches, and SyGuS was first described in [1]. This paper describes concretely the input format of a SyGuS solver. [1] Rajeev Alur, Rastislav Bodik, Garvit Juniwal, Milo M. K. Martin, Mukund Raghothaman, Sanjit A. Seshia, Rishabh Singh, Armando Solar-Lezama, Emina Torlak, and Abhishek Udupa. Syntax-guided synthesis. In FMCAD, pages 1--17, 2013.
Two simple full-text indexes based on the suffix array
Venue: arXiv cs.DS 2016
Year: 2016

We propose two suffix array inspired full-text indexes. One, called SA-hash, augments the suffix array with a hash table to speed up pattern searches due to significantly narrowed search interval before the binary search phase. The other, called FBCSA, is a compact data structure, similar to M{ä}kinen's compact suffix array, but working on fixed sized blocks. Experiments on the Pizza~\&~Chili 200\,MB datasets show that SA-hash is about 2--3 times faster in pattern searches (counts) than the standard suffix array, for the price of requiring $0.2n-1.1n$ bytes of extra space, where $n$ is the text length, and setting a minimum pattern length. FBCSA is relatively fast in single cell accesses (a few times faster than related indexes at about the same or better compression), but not competitive if many consecutive cells are to be extracted. Still, for the task of extracting, e.g., 10 successive cells its time-space relation remains attractive.