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This paper considers a passive localization scenario relying on a single transmitter, several receivers, and multiple moving targets to be located. The so-called “passive” targets equipped with RFID reflectors are capable of reflecting the signals from the transmitter to the receivers. Existing approaches assume that the transmitter and receivers are synchronous or quasi-synchronous, which is not always realistic in practical scenarios. Hence, an asynchronous wireless network is considered, where different clock offsets are assumed at different receivers. We propose a centralized expectation–maximization-based passive localization method for asynchronous receivers (EMpLaR) by treating the clock offsets as hidden variables. Thereby, the proposed algorithm makes use of Taylor expansions to arrive at a closed-form maximization. Furthermore, to improve the robustness to link failures and to reduce the energy consumption, we propose a distributed localization approach based on average consensus formulation to locate the target at each receiver. By applying a quadratic polynomial approximation of the function on which consensus has to be reached, both the computational complexity and the communications overhead are significantly reduced. The Cramér–Rao bound of the target location is derived as a benchmark of our proposed algorithms. Our simulation results show that the proposed centralized and distributed EMpLaR algorithms match the Cramér–Rao bound and significantly improve the localization performance compared with the conventional methods. [ABSTRACT FROM AUTHOR]

Highlights • Algorithm for calibration of car-following model for large-scale microscopic network models. • City-scale case study is carried out, the approach is shown to be computationally efficient and suitable for large-scale network models. • Compared to a traditional approach, it improves the objective function by two orders of magnitude and it improves the fit to link speeds by one order of magnitude. Abstract This paper proposes a simulation-based optimization methodology for the efficient calibration of microscopic traffic flow models (i.e., car-following models) of large-scale stochastic network simulators. The approach is a metamodel simulation-based optimization (SO) method. To improve computational efficiency of the SO algorithm, problem-specific and simulator-specific structural information is embedded into a metamodel. As a closed-form expression is sought, we propose adopting the steady-state solution of the car-following model as an approximation of its simulation-based input-output mapping. This general approach is applied for the calibration of the Gipps car-following model embedded in a microscopic traffic network simulator, on a large network. To this end, a novel formulation for the traffic stream models corresponding to the Gipps car-following law is provided. The proposed approach identifies points with good performance within few simulation runs. Comparing its performances to that of a traditional approach, which does not take advantage of the structural information, the objective function is improved by two orders of magnitude in most experiments. Moreover, this is achieved within tight computational budgets, i.e., few simulation runs. The solutions identified improve the fit to the field measurements by one order of magnitude, on average. The structural information provided to the metamodel is shown to enable the SO algorithm to become robust to both the quality of the initial points and the simulator stochasticity. [ABSTRACT FROM AUTHOR]

We investigate the problem of equilibrium computation for "large" n-player games. Large games have a Lipschitz-type property that no single player's utility is greatly affected by any other individual player's actions. In this paper, we mostly focus on the case where any change of strategy by a player causes other players' payoffs to change by at most 1n. We study algorithms having query access to the game's payoff function, aiming to find ε-Nash equilibria. We seek algorithms that obtain ε as small as possible, in time polynomial in n. Our main result is a randomised algorithm that achieves ε approaching 18 for 2-strategy games in a completely uncoupled setting, where each player observes her own payoff to a query, and adjusts her behaviour independently of other players' payoffs/actions. O(log n) rounds/queries are required. We also show how to obtain a slight improvement over 18, by introducing a small amount of communication between the players. Finally, we give extension of our results to large games with more than two strategies per player, and alternative largeness parameters. [ABSTRACT FROM AUTHOR]

Abstract: Vulnerability metrics play a key role in the understanding of cascading failures and target/random attacks to a network. The graph fragmentation problem (GFP) is the result of a worst‐case analysis of a random attack. We can choose a fixed number of individuals for protection, and a nonprotected target node immediately destroys all reachable nodes. The goal is to minimize the expected number of destroyed nodes in the network. In this paper, we address the GFP by several approaches: metaheuristics, approximation algorithms, polytime methods for specific instances, and exact methods for small instances. The computational complexity of the GFP is included in our analysis, where we formally prove that the corresponding decision version of the problem is NP‐complete. Furthermore, a strong inapproximability result holds: there is no polynomial approximation algorithm with factor lower than 5/3, unless P = NP. This promotes the study of specific instances of the problem for tractability and/or exact methods in exponential time. As a synthesis, we propose new vulnerability/connectivity metrics and an interplay with game theory using a closely related combinatorial problem called component order connectivity. [ABSTRACT FROM AUTHOR]

This paper considers the reconstruction of a discrete-valued random vector from possibly underdetermined linear measurements using sum-of-absolute-value (SOAV) optimization. The proposed algorithm, referred to as discreteness-aware approximate message passing (DAMP), is based on the idea of approximate message passing (AMP), which has been originally proposed for compressed sensing. The DAMP algorithm has low computational complexity and its performance in the large system limit can be predicted analytically via state evolution framework, where we provide a condition for the exact reconstruction with DAMP in the noise-free case. From the analysis, we also propose a method to determine the parameters of the SOAV optimization. Moreover, based on the state evolution, we provide Bayes optimal DAMP, which has the minimum mean-square-error at each iteration of the algorithm. Simulation results show that the DAMP algorithms can reconstruct the discrete-valued vector from underdetermined linear measurements and the empirical performance agrees with our theoretical results in large-scale systems. When the problem size is not large enough, the SOAV optimization with the proposed parameters can achieve better performance than the DAMP algorithms for high signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

In this paper, a versatile solver of a nonconformal volume integral equation based on the Schaubert-Wilton-Glisson (SWG) basis function is presented. Instead of using a piecewise constant function, the robust conventional SWG basis function is chosen and used directly for discontinuous boundaries. A new map method technique is proposed for constructing SWG pairs, which reduces the complexity from ON2 to ONlogN compared with a brute-force method. The integral equation is solved by the method of moments (MoM) and further accelerated by the multilevel fast multipole algorithm (MLFMA). What's more, the hybrid scheme of MLFMA and adaptive cross approximation (ACA) is developed to resolve the low-frequency (LF) breakdown when dealing with over-dense mesh objects. Numerical results show that when in analysis of radiation or scattering problems from inhomogeneous dielectric objects or in LF conditions, the proposed solver shows high efficiency without loss of accuracy, which demonstrates the versatile performance of the proposed method. [ABSTRACT FROM AUTHOR]

The traditional degree distribution framework is a useful tool to analyze irregular low density parity check (LDPC) code. However, it cannot be used to analyze raptor-like LDPC code as it cannot describe the most important structural feature of raptor-like LDPC code, which is that any check node is connected to at most one degree-one variable node. In this paper, we propose a two-type degree distribution framework for raptor-like LDPC code. The proposed framework can describe the special structural feature of raptor-like LDPC code by dividing the check nodes into two different sets. One is the set of check nodes connected to those degree-one variable nodes, the other is the set of check nodes unconnected to those degree-one variable nodes. Furthermore, we propose a two-type discrete density evolution algorithm and a two-type Gaussian approximation density evolution algorithm based on the proposed two-type degree distribution framework to estimate the threshold of raptor-like LDPC code. During the decoding analysis, the proposed algorithms treat the check nodes belonging the two separate sets differently. Compared with the traditional multi-edge type (MET) algorithm, the proposed algorithms allow us to calculate the threshold more quickly without much sacrifice in accuracy. For some raptor-like LDPC codes adopted by the Advanced Television Systems Committee 3.0 (ATSC3.0) standard, the thresholds estimated by the proposed algorithms can be very close to the thresholds estimated by the traditional MET algorithm. The deviations are less than 0.07 dB. Meanwhile, the proposed algorithms can tremendously reduce the computation complexity because of the two-type degree distribution framework and the Gaussian approximation. [ABSTRACT FROM AUTHOR]

Linear detectors, such as zero forcing (ZF) and minimum mean-square error (MMSE), can achieve near-optimum performance due to the favorable channel propagation of massive multiple-input multiple-output systems. However, these detectors employ, in general, exact matrix inversion, which is computationally complex for such huge systems. Thus, in order to avoid the computation of the exact matrix inversion of ZF or MMSE, Newton–Schultz iterative (NSI) algorithm for obtaining an approximate matrix inversion is proposed, which yields similar performance of the exact matrix inversion. Besides, in order to further accelerate the convergence rate and reduce the complexity, we propose a novel initial matrix inversion solution for NSI algorithm based on Tchebychev polynomial, which is much closer to the final exact matrix inverse than the traditional initial matrix inversion solutions. Simulation results show that NSI algorithm with the proposed initial matrix inversion solution achieves the near-optimum ZF performance in just two iterations. Finally, the band matrix concept is employed in order to reduce the computational complexity from $O\left(N_T^3 \right)$ to $O\left(N_T^2 \right)$ , especially when the number of transmitting antennas, $N_T$ , is large. [ABSTRACT FROM AUTHOR]

Abstract We present a (1 + 3 + ϵ) -approximation algorithm for the k -median problem with uniform penalties, extending the recent result by Li and Svensson for the classical k -median problem without penalties. One important difference of this work from that of Li and Svensson is a new definition of sparse instance to exploit the combinatorial structure of our problem. [ABSTRACT FROM AUTHOR]

In the past decades, there has been a burst of activity to simplify implementation of complex software systems. The solution framework in software engineering community for this problem is called component-based software design (CBSD), whereas in the modeling and simulation community it is called composability. Composability is a complex feature due to the challenges of creating components, selecting combinations of components, and integrating the selected components. In this paper, we address the challenge through the analysis of Component Selection (CS), the NP-complete process of selecting a minimal set of components to satisfy a set of objectives. Due to the computational complexity of CS, we consider approximation algorithms that make the component selection process practical. We define three variations of CS and present good approximation algorithms to find near optimal solutions. In spite of our creation of approximable variants of Component Selection, we prove that the general Component Selection problem is inapproximable. [ABSTRACT FROM AUTHOR]

We consider two-player zero-sum stochastic mean payoff games with perfect information. We show that any such game, with a constant number of random positions and polynomially bounded positive transition probabilities, admits a polynomial time approximation scheme, both in the relative and absolute sense. [ABSTRACT FROM AUTHOR]

We study the problem of assigning transmission ranges to radio stations in the plane such that any pair of stations can communicate within a bounded number of hops h and the cost of the network is minimized. We consider two settings of the problem: collinear station locations and arbitrary locations. For the case of collinear stations, we introduce the pioneer polynomial-time exact algorithm for any α≥1 and constant h, and thus conclude that the 1D version of the problem, where h is a constant, is in P. Furthermore, we provide a 3 / 2-approximation algorithm for the case where h is an arbitrary number and α=1, improving the previously best known approximation ratio of 2. For the case of stations placed arbitrarily in the plane and α=1, we first present a (1.5+ε)-approximation algorithm for a case where a deviation of one hop (h+1 hops in total) is acceptable. Then, we show a (3+ε)-approximation algorithm that complies with the exact hop bound. To achieve that, we introduce the following two auxiliary problems, which are of independent interest. The first is the bounded-hop multi-sink range problem, for which we present a PTAS which can be applied to compute a (1+ε)-approximation for the bounded diameter minimum spanning tree, for any ε>0. The second auxiliary problem is the bounded-hop dual-sink pruning problem, for which we show a polynomial-time algorithm. To conclude, we consider the initial bounded-hop all-to-all range assignment problem and show that a combined application of the aforementioned problems yields the (3+ε)-approximation ratio for this problem, which improves the previously best known approximation ratio of 4(9h-2)/(2h-1). [ABSTRACT FROM AUTHOR]

Assortment optimization has received significant attention in recent revenue management and combinatorial optimization literature. In "The Approximability of Assortment Optimization Under Ranking Preferences," A. Aouad, V. Farias, R. Levi, and D. Segev provide best-possible approximability bounds for this problem under an almost general model specification, where preferences are expressed as a distribution over rankings. This paper shows how this optimization problem relates to the computational task of detecting large independent sets in graphs, allowing the establishment of strong complexity lower bounds with respect to various problem parameters. These findings are complemented by a number of algorithms that attain essentially best-possible approximation factors, proving that the hardness results are tight up to lower-order terms. Surprisingly, their results imply that a simple and widely studied policy, known as revenue-ordered assortments, achieves the best possible performance guarantee with respect to prices. The main contribution of this paper is to provide best-possible approximability bounds for assortment planning under a general choice model, where customer choices are modeled through an arbitrary distribution over ranked lists of their preferred products, subsuming most random utility choice models of interest. From a technical perspective, we show how to relate this optimization problem to the computational task of detecting large independent sets in graphs, allowing us to argue that general ranking preferences are extremely hard to approximate with respect to various problem parameters. These findings are complemented by a number of approximation algorithms that attain essentially best-possible factors, proving that our hardness results are tight up to lower-order terms. Surprisingly, our results imply that a simple and widely studied policy, known as revenue-ordered assortments, achieves the best possible performance guarantee with respect to the price parameters. [ABSTRACT FROM AUTHOR]

For the full-bridge LLC converter, it is necessary to establish a large signal model with low-complexity and high-precision when the current of filter inductor works under the continuous conduction mode (CCM) situation. In terms of low complexity, peak values of resonant state variables and average values of slow state variables are taken as the measured indexes between models and actual converter. Models based on the first harmonic approximation (FHA) are studied in depth because they have lower complexity than the existing models. From prospective of high precision, deficiencies of typical FHA model are explained in the light of harmonic generation mechanism of primary current and influence of Fourier series on the typical equivalent circuit. Therefore, transient process of each metallic oxide semiconductor field effect transistor (MOSFET) and its related fast recovery diode, transient process of Schottky rectifier diodes, piecewise equivalent circuit, appropriate selection of variables, and simplified modified dynamic equations are all considered. Furthermore, the unified proposed model is achieved according to the equivalent principle of indexes between aforementioned improved analyses and proposed model. Numerical results of typical FHA model and proposed model are given in accordance with the key indexes. Then, corresponding experimental results are also presented. Differences of indexes between the two models and the actual converter are compared respectively. Though complexity of proposed model is the same as that of typical FHA model, precision of proposed model is higher than that of typical FHA model. [ABSTRACT FROM AUTHOR]

The min-sum algorithm (MSA) for decoding Low-Density Parity-Check (LDPC) code is an approximation algorithm that can greatly reduce the computational complexity of the belief propagation algorithm (BPA). To reduce the error between MSA and BPA, an improved MSA such as normalized min-sum algorithm (NMSA) that uses the normalization factor when updating the check node is used in many LDPC decoders. When obtaining an optimal normalization factor, density evolution (DE) is usually used. However, not only does the DE method require a large number of calculations, it may not be optimal for obtaining a normalization factor due to the theoretical assumptions that need to be satisfied. This paper proposes a new method obtaining a normalization factor for NMSA. We first examine the relationship between the minimum value of variable node messages’ magnitudes and the magnitudes of check node outputs of BPA using the check node message distribution (CMD) chart. And then, we find a normalization factor that minimizes the error between the magnitudes of check node output of NMSA and BPA. We use the least square method (LSM) to minimize the error. Simulation on ATSC 3.0 LDPC codes demonstrates that the normalization factor obtained by this proposed method shows better decoding performance than the normalization factor obtained by DE. [ABSTRACT FROM AUTHOR]

Abstract We consider the following problem in which a given number of items has to be chosen from a predefined set. Each item is described by a vector of attributes and for each attribute there is a desired distribution that the selected set should have. We look for a set that fits as much as possible the desired distributions on all attributes. An example of application is the choice of members for a representative committee, where candidates are described by attributes such as gender, age and profession, and where we look for a committee that for each attribute offers a certain representation, i.e., a single committee that contains a certain number of young and old people, certain number of men and women, certain number of people with different professions, etc. Another example of application is the selection of a common set of items to be used by a group of users, where items are labelled by attribute values. With a single attribute the problem collapses to the apportionment problem for party-list proportional representation systems (in such a case the value of the single attribute would be a political affiliation of a candidate). We study the properties of the associated subset selection rules, as well as their computational complexity. [ABSTRACT FROM AUTHOR]

A physics-based rank-revealing multilevel algorithm to more efficiently compute low-rank (LR) approximations of the method of moments matrix blocks ${\mathbf{Z}}^{\textrm {os}}$ is presented. Using surface subsets of volumetric nonuniform spherical grids (proxy grids), an LR approximation ${\mathbf{Z}}^{\textrm {os}}\approx {\mathbf{AB}}^{\dagger }$ is obtained in two stages: 1) an upward pass and a downward pass on a multilevel tree, via truncated singular value decomposition-based analyses of interactions between source subclusters and their attendant proxy grids, rapidly estimates the rank and yields a domain of ${\mathbf{Z}}^{\textrm {os}}$ , in the form of a matrix ${\mathbf{B}}$ with orthonormal columns and 2) a fast matrix–matrix multiplication step yields ${\mathbf{A}}$. The algorithm reduces the ${\mathcal{ O}}(N^{3})$ computational costs of revealing the rank to ${\mathcal{ O}}(N^{2})$ or ${\mathcal{ O}}(N^{3/2})$ operations and that of finding an LR approximation to ${\mathcal{ O}}(N^{2})$ or ${\mathcal{ O}}(N^{3/2}\log N)$ operations by adopting enclosing or belt-like proxy grids for electromagnetically large basis/testing function distributions that are either densely packed in a volume or quasi-planar, respectively. [ABSTRACT FROM AUTHOR]

In retail, assortment planning refers to selecting a subset of products to offer that maximizes profit. Assortments can be planned for a single store or a retailer with multiple chain stores where demand varies between stores. In this paper, we assume that a retailer with a multitude of stores wants to specify her offered assortment. To suit all local preferences, regionalization and store-level assortment optimization are widely used in practice and lead to competitive advantages. When selecting regionalized assortments, a trade-off between expensive, customized assortments in every store and inexpensive, identical assortments in all stores that neglect demand variation is preferable. We formulate a stylized model for the regionalized assortment planning problem (APP) with capacity constraints and given demand. In our approach, a common assortment that is supplemented by regionalized products is selected. While products in the common assortment are offered in all stores, products in the local assortments are customized and vary from store to store. The model is both applicable for optimizing a total assortment as well as a particular category of an assortment. Concerning the computational complexity, we show that the APP is strongly NP-hard. We formulate the APP as an integer program and provide algorithms and methods for obtaining approximate solutions and solving large-scale instances. Moreover, we extend our model to include substitution effects. Lastly, we perform computational experiments to analyze the benefits of regionalized assortment planning depending on the variation in customer demands between stores. [ABSTRACT FROM AUTHOR]

We propose an evolution strategy algorithm using a sparse plus low rank model for large-scale optimization in this paper. We first develop a rank one evolution strategy using a single principal search direction. It is of linear complexity. Then we extend it to multiple search directions, and develop a rank- ${m}$ evolution strategy. We illustrate that the principal search direction accumulates the natural gradients with respect to the distribution mean, and acts as a momentum term. Further, we analyze the optimal low rank approximation to the covariance matrix, and experimentally show that the principal search direction can effectively learn the long valley of the function with predominant search direction. Then we investigate the effects of Hessian on the algorithm performance. We conduct experiments on a class of test problems and the CEC’2010 LSGO benchmarks. The experimental results validate the effectiveness of our proposed algorithms. [ABSTRACT FROM AUTHOR]

This letter aims at introducing the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not necessarily defined by concave and/or convex functions. An iterative algorithm that is provably convergent and enjoys asymptotic optimality properties is proposed. Numerical results are used to validate its accuracy in the nonasymptotic regime when applied to the energy efficiency maximization in multiuser multiple-input multiple-output communication systems. [ABSTRACT FROM AUTHOR]

An algorithm for the estimation of multiple targets from partial and corrupted observations is introduced based on the concept of a partially distinguishable multitarget system. It combines the advantages of engineering solutions like multiple hypothesis tracking with the rigor of point-process-based methods. It is demonstrated that under intuitive assumptions and approximations, the complexity of the proposed multitarget estimation algorithm can be made linear in terms of the number of tracks and the number of observations, while naturally preserving distinct tracks for detected targets, unlike point-process-based methods. [ABSTRACT FROM AUTHOR]

This paper presents an approximate minimum mean squared error (MMSE) adaptive beam-pattern design (ABD) method for MIMO active sensing systems. The proposed approximate MMSE ABD method leverages the physics of the MIMO arrays to provide a linear-Gaussian approximation that is specific to MIMO active sensing systems, and yields a computationally simple optimization problem. Computational complexity analysis confirms this theoretical reduction in the number of floating-point operations required, most notably that evaluation of the proposed approximate optimization cost function grows polynomially with the number of targets being tracked, whereas for evaluation of the exact cost the growth is exponential. Additionally, numerical results indicate that, even for a simple scenario with a single target being tracked, the proposed approximate MMSE ABD method does indeed reduce the mean squared error of target parameter estimation compared to the nonadaptive case, with a reduction in computation time of four orders of magnitude compared to exact MMSE ABD. [ABSTRACT FROM AUTHOR]

Large graphs are scale-free, ubiquitous having irregular relationships and non-trivial topology. Frequent subgraph mining is a popular method for knowledge extraction from graphs. Most of the existing frequent subgraph mining algorithms are centralized algorithms that cannot handle a single large graph efficiently and incur high communication cost. However, to make the task of subgraph mining less expensive computationally, approximate subgraph mining can be applied which will capture similar structure subgraphs as of exact subgraph mining. In this paper, we propose an approximate subgraph mining algorithm named Ap-FSM implemented on distributed graph environment Pregel. The working of Ap-FSM is divided into three phases. The first phase selects the representative graph from the original graph while preserving the original graph properties. The second phase efficiently performs subgraph extension. Phase 3 introduces a novel two-step optimization for performing subgraph pruning. Analyzing such large graph data will be beneficial from the perspective of expert and intelligent systems, as discovered patterns can be used for knowledge discovery and decision making. To evaluate the performance of Ap-FSM, experiments are performed over three real life datasets having up to billion edges. The results show that the proposed Ap-FSM significantly outperforms the state-of-art frequent subgraph mining algorithms and overcome the challenges of performing frequent subgraph mining on a massive large graph. It is also shown that Ap-FSM achieves high scalability and speedup in distributed graph environment and is highly accurate in finding frequent subgraphs from a single large graph. [ABSTRACT FROM AUTHOR]

We propose a novel filter-type equalizer to improve the solution of the linear minimum-mean squared-error (LMMSE) turbo equalizer, with computational complexity constrained to be quadratic in the filter length. When high-order modulations and/or large memory channels are used, the optimal BCJR equalizer is unavailable, due to its computational complexity. In this scenario, the filter-type LMMSE turbo equalization exhibits a good performance compared to other approximations. In this paper, we show that this solution can be significantly improved by using expectation propagation (EP) in the estimation of the a posteriori probabilities. First, it yields a more accurate estimation of the extrinsic distribution to be sent to the channel decoder. Second, compared to other solutions based on EP, the computational complexity of the proposed solution is constrained to be quadratic in the length of the finite impulse response. In addition, we review the previous EP-based turbo equalization implementations. Instead of considering default uniform priors, we exploit the outputs of the decoder. Some simulation results are included to show that this new EP-based filter remarkably outperforms the turbo approach of the previous versions of the EP algorithm and also improves the LMMSE solution, with and without turbo equalization. [ABSTRACT FROM AUTHOR]

Classical clustering problems search for a partition of objects into a fixed number of clusters. In many scenarios, however, the number of clusters is not known or necessarily fixed. Further, clusters are sometimes only considered to be of significance if they have a certain size. We discuss clustering into sets of minimum cardinality k without a fixed number of sets and present a general model for these types of problems. This general framework allows the comparison of different measures to assess the quality of a clustering. We specifically consider nine quality-measures and classify the complexity of the resulting problems with respect to k. Further, we derive some polynomial-time solvable cases for k=2 with connections to matching-type problems which, among other graph problems, then are used to compute approximations for larger values of k. [ABSTRACT FROM AUTHOR]

High efficiency video coding (HEVC) fractional interpolation algorithm has very high computational complexity. In this paper, two approximate HEVC fractional interpolation filters are proposed. They significantly reduce computational complexity of HEVC fractional interpolation with a negligible PSNR loss and bit rate increase. In addition, two approximate HEVC fractional interpolation hardware are proposed. They, in the worst case, can process 45 quad full HD (${3840\times 2160}$) fps. They consume up to 67.1% less energy than original HEVC fractional interpolation hardware. Therefore, they can be used in consumer electronics products that require a low energy HEVC encoder. [ABSTRACT FROM AUTHOR]

The task of labeling samples is demanding and expensive. Active learning aims to generate the smallest possible training data set that results in a classifier with high performance in the test phase. It usually consists of two steps of selecting a set of queries and requesting their labels. Among the suggested objectives to score the query sets, information theoretic measures have become very popular. Yet among them, those based on Fisher information (FI) have the advantage of considering the diversity among the queries and tractable computations. In this work, we provide a practical algorithm based on Fisher information ratio to obtain query distribution for a general framework where, in contrast to the previous FI-based querying methods, we make no assumptions over the test distribution. The empirical results on synthetic and real-world data sets indicate that this algorithm gives competitive results. [ABSTRACT FROM AUTHOR]

With the advent of the age of big data, a typical big data set called limited labeled big data appears. It includes a small amount of labeled data and a large amount of unlabeled data. Some existing neighborhood-based rough set algorithms work well in analyzing the rough data with numerical features. But, they face three challenges: limited labeled property of big data, computational inefficiency and over-fitting in attribute reduction when dealing with limited labeled data. In order to address the three issues, a combination of neighborhood rough set and local rough set called local neighborhood rough set (LNRS) is proposed in this paper. The corresponding concept approximation and attribute reduction algorithms designed with linear time complexity can efficiently and effectively deal with limited labeled big data. The experimental results show that the proposed local neighborhood rough set and corresponding algorithms significantly outperform its original counterpart in classical neighborhood rough set. These results will enrich the local rough set theory and enlarge its application scopes. [ABSTRACT FROM AUTHOR]

In the Canadian traveler problem, we are given an edge weighted graph with two specified vertices s and t and a probability distribution over the edges that tells which edges are present. The goal is to minimize the expected length of a walk from s to t . However, we only get to know whether an edge is active the moment we visit one of its incident vertices. Under the assumption that the edges are active independently, we show NP-hardness on series-parallel graphs and give results on the adaptivity gap. We further show that this problem is NP-hard on disjoint-path graphs and cactus graphs when the distribution is given by a list of scenarios. We also consider a special case called the multi-target graph search problem. In this problem, we are given a probability distribution over subsets of vertices. The distribution specifies which set of vertices has targets. The goal is to minimize the expected length of the walk until finding a target. For the independent decision model, we show that the problem is NP-hard on trees and give a ( 3.59 + ϵ ) -approximation for trees and a ( 14.4 + ϵ ) -approximation for general metrics. For the scenario model, we show NP-hardness on star graphs. [ABSTRACT FROM AUTHOR]

Local modular control (LMC) is an approach to the supervisory control theory (SCT) of discrete-event systems that exploits the modularity of plant and specifications. Recently, distinguishers and approximations have been associated with SCT to simplify modeling and reduce synthesis effort. This paper shows how advantages from LMC, distinguishers, and approximations can be combined. Sufficient conditions are presented to guarantee that local supervisors computed by our approach lead to the same global closed-loop behavior as the solution obtained with the original LMC, in which the modeling is entirely handled without distinguishers. A further contribution presents a modular way to design distinguishers and a straightforward way to construct approximations to be used in local synthesis. An example of manufacturing system illustrates our approach. Note to Practitioners—Distinguishers and approximations are alternatives to simplify modeling and reduce synthesis cost in SCT, grounded on the idea of event-refinements. However, this approach may entangle the modular structure of a plant, so that LMC does not keep the same efficiency. This paper shows how distinguishers and approximations can be locally combined such that synthesis cost is reduced and LMC advantages are preserved. [ABSTRACT FROM AUTHOR]

A top-k dominating query returns $k$ data objects that dominate the highest number of data objects in a given dataset. This query provides us with a set of intuitively preferred data, thus can support a wide variety of multi-criteria decision-making applications, e.g., e-commerce and web search. Due to the growth of data centers and cloud computing infrastructures, the above applications are increasingly being operated in distributed environments. These motivate us to address the problem of distributed top-k dominating query processing. We propose an efficient decentralized algorithm that exploits virtual points and returns the exact answer. The virtual points are utilized to focus on the data space to be preferentially searched and also to limit the search space to prune unnecessary computation and data forwarding. We also propose two other algorithms, which return an approximate answer set while further reducing query processing time. Extensive experiments on both real and synthetic data demonstrate the efficiency and scalability of our algorithms. [ABSTRACT FROM PUBLISHER]

Sparsity-based subspace clustering algorithms have attracted significant attention thanks to their excellent performance in practical applications. A prominent example is the sparse subspace clustering (SSC) algorithm by Elhamifar and Vidal, which performs spectral clustering based on an adjacency matrix obtained by sparsely representing each data point in terms of all the other data points via the Lasso. When the number of data points is large or the dimension of the ambient space is high, the computational complexity of SSC quickly becomes prohibitive. Dyer et al. observed that SSC-orthogonal matching pursuit (OMP) obtained by replacing the Lasso by the greedy OMP algorithm results in significantly lower computational complexity, while often yielding comparable performance. The central goal of this paper is an analytical performance characterization of SSC-OMP for noisy data. Moreover, we introduce and analyze the SSC-matching pursuit (MP) algorithm, which employs MP in lieu of OMP. Both SSC-OMP and SSC-MP are proven to succeed even when the subspaces intersect and when the data points are contaminated by severe noise. The clustering conditions we obtain for SSC-OMP and SSC-MP are similar to those for SSC and for the thresholding-based subspace clustering (TSC) algorithm due to Heckel and Bölcskei. Analytical results in combination with numerical results indicate that both SSC-OMP and SSC-MP with a data-dependent stopping criterion automatically detect the dimensions of the subspaces underlying the data. Experiments on synthetic and on real data show that SSC-MP often matches or exceeds the performance of the computationally more expensive SSC-OMP algorithm. Moreover, SSC-MP compares very favorably to SSC, TSC, and the nearest subspace neighbor algorithm, both in terms of clustering performance and running time. In addition, we find that, in contrast to SSC-OMP, the performance of SSC-MP is very robust with respect to the choice of parameters in the stopping criteria. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a new multi-edge metric-constrained quasi-cyclic progressive edge-growth algorithm (MM-QC-PEGA), which is suitable for constructing both single- and multi-weighted (binary) QC low-density parity-check (LDPC) codes with arbitrary lengths, rates, circulant sizes, and variable node (VN)-degree distributions. The MM-QC-PEGA is able to detect all cyclic-edge-set-minimum-virtual cycles (CMVCs), as it accurately computes the metric value of each CMVC with an a posteriori test. In addition, we propose a new greatest-common-divisor (GCD)-approximation for time efficiently approximating the metric value of a CMVC without a posteriori tests, and propose a new GCD-approximated MM-QC-PEGA (G-MM-QC-PEGA) by using the GCD-approximation to replace the a posteriori test involved in the MM-QC-PEGA. As a result, the G-MM-QC-PEGA is faster than the MM-QC-PEGA, and the CMVCs undetectable to the G-MM-QC-PEGA under multi- and single-weighted QC-LDPC code graphs have minimum lengths of eight and ten, respectively. Moreover, we propose a new masking technique that is efficient in masking the parity-check matrix consisting of an array of arbitrary circulants of the same size. Compared with the several existing works, our proposed algorithms could perform better or comparably in terms of avoiding generating small cycles and error performances. Our proposed algorithms somewhat perfect the works of QC-LDPC code construction. [ABSTRACT FROM PUBLISHER]

Energy efficiency is lately a major concern for computer engineers, at the levels of both software and hardware. A popular path is the exploitation of heterogeneity and accelerator-based systems, which combine different architectures, each appropriate for specific computational patterns. Approximate computing is another aggressive, yet viable alternative; it minimizes the energy footprint of applications at the expense of output quality.We introduce AcHEe, a set of 12 applications – ranging from real-world applications to kernels – from different domains, exposing a wide range of characteristics, which have been modified to exploit both heterogeneity and approximations. The degree of approximation can be controlled at runtime. The implementation is based on OpenCL and is publicly available.We evaluate these applications on heterogeneous platforms (comprising of CPUs and GPUs) and quantify the isolated and combined effect of heterogeneous and approximate computing. AcHEe can serve as a benchmark suite, to evaluate current and future computational devices from the perspective of heterogeneity and approximations. At the same time, it can serve as a software platform to evaluate and compare different approximation techniques. [ABSTRACT FROM AUTHOR]

Latin Hypercube Designs (LHDs) are crucial in the meta-modeling field. An LHD with maximal minimum distance between any pair of points guarantees a high quality of the model. We introduce a generalization of the Maximin LHD construction, the Maximin LHD completion, in which some points of the design are already fixed. We study the complexity of this problem and prove that it is NP-complete and it does not admit any approximation algorithm in most practical cases. [ABSTRACT FROM AUTHOR]

Comparative genomics is a line of study which aims at determining dis/similarities between genomes. One way of doing this is to infer the large scale mutations (also called genome rearrangements ) that are responsible for transforming one genome into another, under the parsimony principle. Numerous efforts have been made over the past years regarding the traditional approach, in which all genome rearrangements have the same unit cost . However, since long rearrangements are more likely to disturb the organism, some works considered the length-weighted approach, in which the cost of each rearrangement is a function of its length. The problem is thus modeled as follows: given two genomes G 1 and G 2 and a set β of allowed genome rearrangements, each with a given cost, determine their distance , i.e., the total cost of a minimum-cost sequence of rearrangements from β that transforms G 1 into G 2 . In this paper, we study length-weighted reversals and transpositions, mainly considering their prefix variants (in which the leftmost part of the genome must always be included). We present approximation algorithms and bounds on the distances and diameters (i.e., maximum possible distance over any two genomes of same length) for eight problems when genomes are represented as permutations, and another eight problems when genomes are represented as binary strings, in each case considering two different cost functions. [ABSTRACT FROM AUTHOR]

Read trimming is a fundamental first step of the analysis of next generation sequencing (NGS) data. Traditionally, it is performed heuristically, and algorithmic work in this area has been neglected. Here, we address this topic and formulate three optimization problems for block-based trimming (truncating the same low-quality positions at both ends for all reads and removing low-quality truncated reads). We find that all problems are NP-hard. Hence, we investigate the approximability of the problems. Two of them are NP-hard to approximate. However, the non-random distribution of quality scores in NGS data sets makes it tempting to speculate that quality constraints for read positions are typically satisfied by fulfilling quality constraints for reads. Thus, we propose three relaxed problems and develop efficient polynomial-time algorithms for them including heuristic speed-up techniques and parallelizations. We apply these optimized block trimming algorithms to 12 data sets from three species, four sequencers, and read lengths ranging from 36 to 101 bp and find that (i) the omitted constraints are indeed almost always satisfied, (ii) the optimized read trimming algorithms typically yield a higher number of untrimmed bases than traditional heuristics, and (iii) these results can be generalized to alternative objective functions beyond counting the number of untrimmed bases. [ABSTRACT FROM PUBLISHER]

BigBand is a technique for wideband spectrum sensing (WSS) that can capture gigahertz of sparse spectrum in real time by using shifted multiple channels without sampling the signal at GS/s. In this paper, we focus on enforcing BigBand with the proposed improved algorithm, namely, AD-BigBand, for efficient and robust computation. AD-BigBand converts the nonlinear process (locating frequency and computing the spectrum value) of sparse WSS into two steps of solving linear equations. In particular, we define an r -degree frequency locator polynomial to rapidly locate nonzero frequencies. The computing complexity of the proposed method decreases from O(K{\log ^2}K ({{{n\log K} \over K}})^{\log K}) of shifted sampling based BigBand to O(K{\log ^2}K)$, where the $K$-sparse signals of bandwitdth $n$ are subsampled with arithmetic time-shifted sensing channels. We implement AD-BigBand on a commercial four-channel acquisition card. Experimental results show that AD-BigBand improves the WSS capabilities and exhibits higher processing speed and lower error spectrum construction rate than BigBand, especially in the case of relative low signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

In Part I, we study a special case of the unweighted Tree Augmentation Problem (TAP) via the Lasserre (Sum of Squares) system. In the special case, we forbid so-called stems; these are a particular type of subtree configuration. For stemless TAP, we prove that the integrality ratio of an SDP relaxation (the Lasserre tightening of an LP relaxation) is ≤32+ϵ, where ϵ>0 can be any small constant. We obtain this result by designing a polynomial-time algorithm for stemless TAP that achieves an approximation guarantee of 32+ϵ relative to the SDP relaxation. The algorithm is combinatorial and does not solve the SDP relaxation, but our analysis relies on the SDP relaxation. We generalize the combinatorial analysis of integral solutions from the previous literature to fractional solutions by identifying some properties of fractional solutions of the Lasserre system via the decomposition result of Karlin et al. (Integer programming and combinatoral optimization (IPCO), Lecture Notes in Computer Science, vol 6655. Springer, Berlin/Heidelberg, pp 301–314, 2011). Also, we present an example of stemless TAP such that the approximation guarantee of 32 is tight for the algorithm. In Part II of this paper, we extend the methods of Part I to prove the same results relative to the same SDP relaxation for TAP. [ABSTRACT FROM AUTHOR]

Recurrent neural network architectures can have useful computational properties, with complex temporal dynamics and input-sensitive attractor states. However, evaluation of recurrent dynamic architectures requires solving systems of differential equations, and the number of evaluations required to determine their response to a given input can vary with the input or can be indeterminate altogether in the case of oscillations or instability. In feedforward networks, by contrast, only a single pass through the network is needed to determine the response to a given input. Modern machine learning systems are designed to operate efficiently on feedforward architectures. We hypothesized that two-layer feedforward architectures with simple, deterministic dynamics could approximate the responses of single-layer recurrent network architectures. By identifying the fixed-point responses of a given recurrent network, we trained two-layer networks to directly approximate the fixed-point response to a given input. These feedforward networks then embodied useful computations, including competitive interactions, information transformations, and noise rejection. Our approach was able to find useful approximations to recurrent networks, which can then be evaluated in linear and deterministic time complexity. [ABSTRACT FROM AUTHOR]

We consider the problem of allocating a set of resources for performing a given collection of jobs. Each of the jobs has specific resource requirement for its execution. Each resource has specific start time, finish time and associated cost per unit usage. The objective is to execute the jobs while incurring minimum cost. The problem is NP-hard. We improve known four-approximation to a three-approximation algorithm. Our algorithm implies better approximation for two other related problems. [ABSTRACT FROM AUTHOR]

Datasets in the fields of climate and environment are often very large and irregularly spaced. To model such datasets, the widely used Gaussian process models in spatial statistics face tremendous challenges due to the prohibitive computational burden. Various approximation methods have been introduced to reduce the computational cost. However, most of them rely on unrealistic assumptions for the underlying process and retaining statistical efficiency remains an issue. We develop a new approximation scheme for maximum likelihood estimation. We show how the composite likelihood method can be adapted to provide different types of hierarchical low rank approximations that are both computationally and statistically efficient. The improvement of the proposed method is explored theoretically; the performance is investigated by numerical and simulation studies; and the practicality is illustrated through applying our methods to two million measurements of soil moisture in the area of the Mississippi River basin, which facilitates a better understanding of the climate variability. Supplementary material for this article is available online. [ABSTRACT FROM AUTHOR]

The recursive least squares algorithm (RLS) using dichotomous coordinate descent (DCD) iterations, namely, RLS-DCD, is regarded to be well suited for hardware implementation because of its small computational complexity compared to the classical RLS algorithm. While this is true, yet another important aspect that ultimately determines its applicability for real-time applications with high sample rates, is its iteration bound. In this brief, we discuss this issue and propose a modified RLS-DCD algorithm based on delay relaxation whose iteration bound can be reduced arbitrarily. The degradation in convergence speed is shown to be tolerable, which results in still much faster convergence compared to the normalized least mean square algorithm. [ABSTRACT FROM PUBLISHER]

In this paper the following selection problem is discussed. A set of n items is given and we wish to choose a subset of exactly p items of the minimum total cost. This problem is a special case of 0–1 knapsack in which all the item weights are equal to 1. Its deterministic version has an O ( n ) -time algorithm, which consists in choosing p items of the smallest costs. In this paper it is assumed that the item costs are uncertain. Two robust models, namely two-stage and recoverable ones, under discrete and interval uncertainty representations, are discussed. Several positive and negative complexity results for both of them are provided. [ABSTRACT FROM AUTHOR]

Graph burning is a model for the spread of social contagion. The burning number is a graph parameter associated with graph burning that measures the speed of the spread of contagion in a graph; the lower the burning number, the faster the contagion spreads. We prove that the corresponding graph decision problem is NP -complete when restricted to acyclic graphs with maximum degree three, spider graphs and path-forests. We provide polynomial time algorithms for finding the burning number of spider graphs and path-forests if the number of arms and components, respectively, are fixed. Finally, we describe a polynomial time approximation algorithm with approximation factor 3 for general graphs. [ABSTRACT FROM AUTHOR]

Graph Distance Contest (GDC) was organized in the context of ICPR 2016. Its main challenge was to inspect and report performances and effectiveness of exact and approximate graph edit distance methods by comparison with a ground truth. This paper presents the context of this competition, the metrics and datasets used for evaluation, and the results obtained by the eight submitted methods. Results are analyzed and discussed in terms of computation time and accuracy. We also highlight the future challenges in graph edit distance regarding both future methods and evaluation metrics. The contest was supported by the Technical Committee on Graph-Based Representations in Pattern Recognition (TC-15) of the International Association of Pattern Recognition (IAPR). [ABSTRACT FROM AUTHOR]

The Resource Allocation Problem with Time Dependent Penalties (RAPTP) is a variant of uncapacitated resource allocation problems generally referred as uncapacitated facility allocation problems or uncapacitated facility location problem (UFLP). Work done in this paper is motivated by the work of Du, Lu and Xu [7] in which authors considered facility location problems with submodular penalties and presented a 3-approximation primal dual algorithm. This paper considers that each unallocated demand point adds to penalty that increases as time passes and is thus represented by function x (t i , p i) where t i and p i are elapse time and priority of demand point d i . As this problem has been considered for emergency service allocation, all demand points should be allocated to some facility or resource within some stipulated time limit beyond which it may lose its purpose. Thus penalty incurred by a demand point is considered till that threshold value only. Thus it is assumed that penalty contribution by a demand point remains constant after a specified threshold value. By exploiting the properties of time dependent penalties, a 4-approximation primal-dual algorithm is proposed which is based on LP framework, and is the first constant-factor approximation algorithm for RAPTP. [ABSTRACT FROM AUTHOR]

We introduce a structured low rank matrix completion algorithm to recover a series of images from their under-sampled measurements, where the signal along the parameter dimension at every pixel is described by a linear combination of exponentials. We exploit the exponential behavior of the signal at every pixel, along with the spatial smoothness of the exponential parameters to derive an annihilation relation in the Fourier domain. This relation translates to a low-rank property on a structured matrix constructed from the Fourier samples. We enforce the low-rank property of the structured matrix as a regularization prior to recover the images. Since the direct use of current low rank matrix recovery schemes to this problem is associated with high computational complexity and memory demand, we adopt an iterative re-weighted least squares algorithm, which facilitates the exploitation of the convolutional structure of the matrix. Novel approximations involving 2-D fast Fourier transforms are introduced to drastically reduce the memory demand and computational complexity, which facilitates the extension of structured low-rank methods to large scale 3-D problems. We demonstrate our algorithm in the MR parameter mapping setting and show improvement over the state-of-the-art methods. [ABSTRACT FROM PUBLISHER]

Connectivity has significance in both of data collection and aggregation for Wireless Sensor Networks (WSNs). Once the connectivity is lost, relay nodes are deployed to build a Steiner Minimal Tree (SMT) such that the inter-component connection is reestablished. In recent years, there has been a growing interest in connectivity restoration problems. In previous works, the deployment area of a WSN is assumed to be flat without obstacles. However, such an assumption is not realistic. In addition, most of the existing strategies chose the representative of each component, which serves as the starting point of relay node deployment during the connectivity restoration, either in a random way or in the shortest-distance based manner. In fact, both ways of representative selection could potentially increase the length of the SMT such that more relay nodes are required. In this paper, a novel connectivity restoration strategy is proposed--Obstacle-Avoid connectivity restoration strategy based on Straight Skeletons (OASS), which employs both the polygon based representative selection with the presence of obstacles and the straight skeleton based SMT establishment. The OASS is proved to be a 3-opt approximation algorithm with the complexity of O(n log n), and the approximation ratio can reduce to 3 p 3 2 while it satisfies a certain condition. The theoretical analysis and simulations show that the performance of the OASS is better than other strategies in terms of the relay count and the quality of the established topology (i.e., distances between components, delivery latency and balanced traffic load) as well. [ABSTRACT FROM AUTHOR]

In the deployment of interval type-2 fuzzy systems, one of the most important steps is the type reduction. The commonly used center of sets type reducer requires the solution of two nonlinear constrained optimization problems. Frequently used approaches to solve them are the Karnik–Mendel algorithms and their variants. However, these algorithms suffer from the need for sorting, which is known to be computationally very expensive. Using the reformulations proposed in this paper for center of sets type reducer, it is possible to eliminate the need for sorting. This makes interval type-2 fuzzy systems more appropriate for cost-sensitive real-time applications. Extensive simulations are presented to illustrate the faster convergence speed of the proposed method over six other enhanced variants of the Karnik–Mendel algorithm as applied to center of sets type reduction of interval type-2 fuzzy systems. [ABSTRACT FROM PUBLISHER]