Linear Complexity Algorithm Research Articles

FatRegion: A Fast Adaptive Tree-Structured Region Extraction Approach

Coherent image regions can be used as good features for many computer vision tasks, such as object tracking, segmentation, and recognition. Most of previous region extraction methods, however, are not suitable for online applications because of their either heavy computations or unsatisfactory results. We propose a seed-based region growing and merging approach to generate simultaneously coherent and discriminative image regions. We present a quadtree-based seed initialization algorithm to adaptively place seeds into different image areas and then grow them into regions by a color- and edge-guided growing procedure. To merge these regions in different levels, we propose to use the generalized boundary strength to measure the quality of region merging result. In addition, we present a region merging algorithm of linear time complexity to perform efficient and effective region merging. Overall, our new approach simultaneously holds these advantages: 1) it is extremely fast with linear complexity in both time and space, which takes less than 50 ms to process an HVGA image; 2) it can give a direct control of the region number and well adapt to image regions with various sizes and shapes; and 3) it provides a tree-structured representation of the regions and thus can model the image from multiple scales. We evaluate the proposed approach on the standard benchmarks with extensive comparisons with the state-of-the-art methods. The experimental results demonstrate its good comprehensive performances. Example applications using the extracted regions as features for online object tracking and multiclass object segmentation also exhibit its potential for many computer vision tasks.

An Energy-Based Model Encoding Nonlocal Pairwise Pixel Interactions for Multisensor Change Detection

Image change detection (CD) is a challenging problem, particularly when images come from different sensors. In this paper, we present a novel and reliable CD model, which is first based on the estimation of a robust similarity-feature map generated from a pair of bitemporal heterogeneous remote sensing images. This similarity-feature map, which is supposed to represent the difference between the multitemporal multisensor images, is herein defined, by specifying a set of linear equality constraints, expressed for each pair of pixels existing in the before-and-after satellite images acquired through different modalities. An estimation of this overconstrained problem, also formulated as a nonlocal pairwise energy-based model, is then carried out, in the least square sense, by a fast linear-complexity algorithm based on a multidimensional scaling mapping technique. Finally, the fusion of different binary segmentation results, obtained from this similarity-feature map by different automatic thresholding algorithms, allows us to precisely and automatically classify the changed and unchanged regions. The proposed method is tested on satellite data sets acquired by real heterogeneous sensor, and the results obtained demonstrate the robustness of the proposed model compared with the best existing state-of-the-art multimodal CD methods recently proposed in the literature.

The minimum-cost transformation of graphs

A complete proof that algorithms proposed by the authors solve the problem of minimum-cost transformation of a graph into another graph is given. The problem is solved both by a direct algorithm of linear complexity and by a reduction to quadratic integer linear programming.

Examining database persistence of ISO/EN 13606 standardized electronic health record extracts: relational vs. NoSQL approaches

BackgroundThe objective of this research is to compare the relational and non-relational (NoSQL) database systems approaches in order to store, recover, query and persist standardized medical information in the form of ISO/EN 13606 normalized Electronic Health Record XML extracts, both in isolation and concurrently. NoSQL database systems have recently attracted much attention, but few studies in the literature address their direct comparison with relational databases when applied to build the persistence layer of a standardized medical information system.MethodsOne relational and two NoSQL databases (one document-based and one native XML database) of three different sizes have been created in order to evaluate and compare the response times (algorithmic complexity) of six different complexity growing queries, which have been performed on them. Similar appropriate results available in the literature have also been considered.ResultsRelational and non-relational NoSQL database systems show almost linear algorithmic complexity query execution. However, they show very different linear slopes, the former being much steeper than the two latter. Document-based NoSQL databases perform better in concurrency than in isolation, and also better than relational databases in concurrency.ConclusionNon-relational NoSQL databases seem to be more appropriate than standard relational SQL databases when database size is extremely high (secondary use, research applications). Document-based NoSQL databases perform in general better than native XML NoSQL databases. EHR extracts visualization and edition are also document-based tasks more appropriate to NoSQL database systems. However, the appropriate database solution much depends on each particular situation and specific problem.

Partial Decode-Forward Relaying for the Gaussian Two-Hop Relay Network

The multicast capacity of the Gaussian two-hop relay network with one source, $N$ relays, and $L$ destinations is studied. It is shown that a careful modification of the partial decode-forward coding scheme, whereby the relays recover and coherently transmit degraded sets of message parts, achieves the cutset upper bound within $(1/2)\log N$ bits regardless of the channel gains and power constraints. This scheme improves upon a previous scheme by Chern and Ozgur, which is also based on partial decode-forward yet has an unbounded gap from the cutset bound for $L \ge 2$ destinations. When restricted to noncoherent transmission among the relays, the proposed partial decode-forward scheme achieves a slightly larger gap of $\log N$ bits from the cutset bound. The computation of this relaxed achievable rate involves evaluating mutual information across $L(N+1)$ cuts out of the total $L 2^{N}$ possible cuts, providing a very simple linear-complexity algorithm to approximate the single-source multicast capacity of the Gaussian two-hop relay network.

An Accurate Pricing Formula for Vanilla Options in a Cash Dividend Framework with Linear Algorithmic Complexity

The aim of this article is to provide a fast and efficient formula to price vanilla options in presence of cash dividends. Bos & Vandermark have provided a simple and intuitive formula but not really accurate for long maturities or for strikes far from the money. Many authors have proposed some accurate formula but with a polynomial (quadratic for Henry-Labordere) algorithmic complexity in the number of dividends. In this article we derive a formula whose accuracy is equivalent to that of Henry-Labordere but with a linear algorithmic complexity, preserving the call-put parity and the continuity of the vanilla price at each ex-dividend dates.

Concurrent optimal allocation of distributed manufacturing resources using extended Teaching-Learning-Based Optimization

The optimal allocation of distributed manufacturing resources is a challenging task for supply chain deployment in the current competitive and dynamic manufacturing environments, and is characterised by multiple objectives including time, cost, quality and risk that require simultaneous considerations. This paper presents an improved variant of the Teaching-Learning-Based Optimisation (TLBO) algorithm to concurrently evaluate, select and sequence the candidate distributed manufacturing resources allocated to subtasks comprising the supply chain, while dealing with the trade-offs among multiple objectives. Several algorithm-specific improvements are suggested to extend the standard form of TLBO algorithm, which is only well suited for the one-dimensional continuous numerical optimisation problem well, to solve the two-dimensional (i.e. both resource selection and resource sequencing) discrete combinatorial optimisation problem for concurrent allocation of distributed manufacturing resources through a focused trade-off within the constrained set of Pareto optimal solutions. The experimental simulation results showed that the proposed approach can obtain a better manufacturing resource allocation plan than the current standard meta-heuristic algorithms such as Genetic Algorithm, Particle Swarm Optimisation and Harmony Search. Moreover, a near optimal resource allocation plan can be obtained with linear algorithmic complexity as the problem scale increases greatly.

Clustering Mixed Data Set by Fuzzy Set Partitioning

K mean clustering is a very popular clustering algorithm for clustering numerical data. . It is popular due to its simplicity of understanding and linear algorithmic complexity measure. But it has the serious limitation of clustering numerical only data. Therefore several researchers tried to improve the k mean algorithm to cluster not only numerical but also categorical dataset. In this work an effort have been made to put forward a proposed FCV mean algorithm which is a modified version of the traditional k-mean algorithm and is able to cluster objects having mixed type attributes i.e. numerical and categorical. For categorical data fuzzy set similarity is used and for numerical data differences from maximum dissimilarity is used. Experiment shows that the mixed data are highly clustered with high accuracy compared to other approach in literature.

Mobility-Enabled Service Selection for Composite Services

Mobile business is becoming a reality due to ubiquitous Internet connectivity, popular mobile devices, and widely available cloud services. However, characteristics of the mobile environment, such as mobility, unpredictability, and variation of mobile network's signal strength, present challenges in selecting optimal services for composition. Traditional QoS-aware methods that select individual services with the best QoS may not always result in the best composite service because constant mobility makes the performance of service invocation unpredictable and location-based. This paper discusses the challenges of this problem and defines it in a formal way. To solve this new research problem, we propose a mobility model, a mobility-aware QoS computation rule, and a mobility-enabled selection algorithm with teaching-learning-based optimization. The experimental simulation results demonstrate that our approach can obtain better solutions than current standard composition methods in mobile environments. The approach can obtain near-optimal solutions and has a nearly linear algorithmic complexity with respect to the problem size.

An algorithm for the spectral immunity of binary sequence with period 2 n

To resist the fast algebraic attack and fast selective discrete Fourier transform attacks, spectral immunity of a sequence or a Boolean function was proposed. At the same time, an algorithm to compute the spectral immunity of the binary sequence with odd period N was presented, here N is a factor of 2 n − 1, where n is an integer. The case is more complicated when the period is even. In this paper, we compute linear complexity of every orthogonal sequence of a given sequence using Chan-Games algorithm and k - error linear complexity algorithm. Then, an algorithm for spectral immunity of binary sequence with period N = 2 n is obtained. Furthermore, the time complexity of this algorithm is proved to be O(n).

Multifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data sets

We develop a framework for multifidelity information fusion and predictive inference in high-dimensional input spaces and in the presence of massive data sets. Hence, we tackle simultaneously the “big N" problem for big data and the curse of dimensionality in multivariate parametric problems. The proposed methodology establishes a new paradigm for constructing response surfaces of high-dimensional stochastic dynamical systems, simultaneously accounting for multifidelity in physical models as well as multifidelity in probability space. Scaling to high dimensions is achieved by data-driven dimensionality reduction techniques based on hierarchical functional decompositions and a graph-theoretic approach for encoding custom autocorrelation structure in Gaussian process priors. Multifidelity information fusion is facilitated through stochastic autoregressive schemes and frequency-domain machine learning algorithms that scale linearly with the data. Taking together these new developments leads to linear complexity algorithms as demonstrated in benchmark problems involving deterministic and stochastic fields in up to $10^{5}$ input dimensions and $10^{5}$ training points on a standard desktop computer.

Computation Offloading for Service Workflow in Mobile Cloud Computing

The development of cloud computing and virtualization techniques enables mobile devices to overcome the severity of scarce resource constrained by allowing them to offload computation and migrate several computation parts of an application to powerful cloud servers. A mobile device should judiciously determine whether to offload computation as well as what portion of an application should be offloaded to the cloud. This paper considers a mobile computation offloading problem where multiple mobile services in workflows can be invoked to fulfill their complex requirements and makes decision on whether the services of a workflow should be offloaded. Due to the mobility of portable devices, unstable connectivity of mobile networks can impact the offloading decision. To address this issue, we propose a novel offloading system to design robust offloading decisions for mobile services. Our approach considers the dependency relations among component services and aims to optimize execution time and energy consumption of executing mobile services. To this end, we also introduce a mobility model and a trade-off fault-tolerance mechanism for the offloading system. A genetic algorithm (GA) based offloading method is then designed and implemented after carefully modifying parts of a generic GA to match our special needs for the stated problem. Experimental results are promising and show near-optimal solutions for all of our studied cases with almost linear algorithmic complexity with respect to the problem size.

Precise Euclidean distance transforms in 3D from voxel coverage representation

Distance transforms (DTs) are, usually, defined on a binary image as a mapping from each background element to the distance between its centre and the centre of the closest object element. However, due to discretization effects, such DTs have limited precision, including reduced rotational and translational invariance. We show in this paper that a significant improvement in performance of Euclidean DTs can be achieved if voxel coverage values are utilized and the position of an object boundary is estimated with sub-voxel precision. We propose two algorithms of linear time complexity for estimating Euclidean DT with sub-voxel precision. The evaluation confirms that both algorithms provide 4–14 times increased accuracy compared to what is achievable from a binary object representation.

The Thinnest Path Problem

We formulate and study the thinnest path problem for secure communication in wireless ad hoc networks. The objective is to find a path from a source to its destination that results in the minimum number of nodes overhearing the message by a judicious choice of relaying nodes and their corresponding transmission powers. We adopt a directed hypergraph model of the problem and establish the NP-completeness of the problem in 2-D networks. We then develop two polynomial-time approximation algorithms that offer √(n/2) and n/2√(n-1) approximation ratios for general directed hypergraphs (which can model nonisotropic signal propagation in space) and constant approximation ratios for ring hypergraphs (which result from isotropic signal propagation). We also consider the thinnest path problem in 1-D networks and 1-D networks embedded in a 2-D field of eavesdroppers with arbitrary unknown locations (the so-called 1.5-D networks). We propose a linear-complexity algorithm based on nested backward induction that obtains the optimal solution for both 1-D and 1.5-D networks. This algorithm does not require the knowledge of eavesdropper locations and achieves the best performance offered by any algorithm that assumes complete location information of the eavesdroppers.

Generalized Rybicki Press algorithm

SummaryThis article discusses a more general and numerically stable Rybicki Press algorithm, which enables inverting and computing determinants of covariance matrices, whose elements are sums of exponentials. The algorithm is true in exact arithmetic and relies on introducing new variables and corresponding equations, thereby converting the matrix into a banded matrix of larger size. Linear complexity banded algorithms for solving linear systems and computing determinants on the larger matrix enable linear complexity algorithms for the initial semi‐separable matrix as well. Benchmarks provided illustrate the linear scaling of the algorithm. Copyright © 2015 John Wiley & Sons, Ltd.

A Posteriori Error Control at Numerical Solution of Plate Bending Problem

The classical approach to a posteriori error control considered in this paper bears on the counter variational principles of Lagrange and Castigliano. Its efficient implementation for problems of mechanics of solids assumes obtaining equilibrated stresses/resultants which, at the same time, are sufficiently close to the exact values. Besides, it is important that computation of the error bound with the use of such stresses/resultants would be cheap in respect to the arithmetic work. Following these guide lines, we expand the preceding results for elliptic partial differential equations and theory elasticity equations upon the problem of thin plate bending. We obtain guaranteed a posteriori error bounds of simple forms for solutions by the finite element method and discuss the algorithms of linear complexity for their computation. The approach of the paper also allows to improve some known general a posteriori estimates by means of arbitrary not equilibrated stress fields.

Adaptive thresholding with inverted triangular area for real-time detection of the heart rate from photoplethysmogram traces on a smartphone.

Photoplethysmogram (PPG) signals acquired by smartphone cameras are weaker than those acquired by dedicated pulse oximeters. Furthermore, the signals have lower sampling rates, have notches in the waveform and are more severely affected by baseline drift, leading to specific morphological characteristics. This paper introduces a new feature, the inverted triangular area, to address these specific characteristics. The new feature enables real-time adaptive waveform detection using an algorithm of linear time complexity. It can also recognize notches in the waveform and it is inherently robust to baseline drift. An implementation of the algorithm on Android is available for free download. We collected data from 24 volunteers and compared our algorithm in peak detection with two competing algorithms designed for PPG signals, Incremental-Merge Segmentation (IMS) and Adaptive Thresholding (ADT). A sensitivity of 98.0% and a positive predictive value of 98.8% were obtained, which were 7.7% higher than the IMS algorithm in sensitivity, and 8.3% higher than the ADT algorithm in positive predictive value. The experimental results confirmed the applicability of the proposed method.

On-Line Fault Diagnosis With Partially Observed Petri Nets

This technical note concerns fault detection and diagnosis for discrete event systems modeled with partially observed Petri nets. The proposed method provides diagnosis decisions via the analysis of observation sequences that include some observable events and the partial measurement of the successive states visited by the system. To this end, the observation sequences are decomposed into elementary observation sequences, linear matrix inequalities are used to compute the firing sequences consistent with each elementary observation sequence and an algorithm of linear complexity with respect to the length of the observation sequences is proposed to provide on-line diagnosis decisions.

Adaptive Sparse Channel Estimation under Symmetric alpha-Stable Noise

We tackle the problem of channel estimation in environments that exhibit both sparse, time-varying impulse responses and impulsive noise with Symmetric alpha-Stable (SαS) statistics. Two novel frameworks are proposed for designing online adaptive algorithms that exploit channel sparseness and achieve robust performance against impulses. The first framework generates recursive least-squares (RLS)-type algorithms based on a differentiable cost function that combines robust nonlinear methods with sparse-promoting L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> norm regularization. The second framework employs the natural gradient (NG) and incorporates non-linear methods for the channel prediction error as well as the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> norm of the channel taps. From these frameworks, we derive linear and quadratic complexity algorithms. The improved performance of the proposed RLS-type and NG-type algorithms relative to conventional robust algorithms, such as the recursive least M-estimate (RLM) algorithm and the recursive least p-norm (RLP) algorithm, is validated by using extensive computer simulations as well as signal analysis from an underwater acoustic communications experiment. In addition, we discovered that RLM is not robust under specific SαS noise conditions, contrary to the claim in\thinspace. Finally, our results also demonstrate the clear superiority of the NG-type algorithms over their RLS-type counterparts.

Fault probability evaluation in DESs with an algorithm of linear complexity and partially observed SPNs

This article concerns fault diagnosis for stochastic discrete event systems. For this purpose, partially observed stochastic Petri nets are introduced that include (i) the Markovian stochastic dynamics used to represent failure processes and also (ii) the model of the sensors used to measure the events and markings. Timed observation sequences result from this modeling and the probabilities of marking trajectories consistent with a given timed observation sequence are systematically computed. Diagnosis in terms of faults probability is obtained as a consequence and an algorithm of linear complexity is proposed to evaluate the fault probability on the basis of segments extracted from the timed observation sequence. Performance of the algorithm is discussed wrt to usual non detection and false alarm rates.