Linear Complexity Algorithm Research Articles

Large Scale LP Decoding with Low Complexity

Linear program (LP) decoding has become increasingly popular for error-correcting codes due to its simplicity and promising performance. Low-complexity and efficient iterative algorithms for LP decoding are of great importance for practical applications. In this paper we focus on solving the binary LP decoding problem by using the alternating direction method of multipliers (ADMM). Our main contribution is that we propose a linear-complexity algorithm for the projection onto a parity polytope (having a computational complexity of small O(d), where small d is the check-node degree), as compared to recent work , which has a computational complexity of small O(d log d). In particular, we show that the projection onto the parity polytope can be transformed to a projection onto a simplex.

A novel method for performance evaluation of text chunking

Evaluation of text chunking is revisited. The proposed method tries to analyze the errors made by a chunker and formulates an evaluation strategy that brings out the strength and weakness of a chunker in a better way than the existing precision, recall and F score based methods or their variants do. A tree-matching based algorithm of linear time complexity is designed, analyzed, and illustrated by giving examples. Correctness of the algorithm is checked by using a chunker and a set of test sentences.

A framework for semi-supervised and unsupervised optimal extraction of clusters from hierarchies

We introduce a framework for the optimal extraction of flat clusterings from local cuts through cluster hierarchies. The extraction of a flat clustering from a cluster tree is formulated as an optimization problem and a linear complexity algorithm is presented that provides the globally optimal solution to this problem in semi-supervised as well as in unsupervised scenarios. A collection of experiments is presented involving clustering hierarchies of different natures, a variety of real data sets, and comparisons with specialized methods from the literature.

An Experimental Comparison of Semi-supervised Learning Algorithms for Multispectral Image Classification

Semi-Supervised Learning (SSL) method has recently caught much attention in the fields of machine learning and computer vision owing to its superiority in classifying abundant unlabelled samples using a few labeled samples. The goal of this paper is to provide an experimental efficiency comparison between graph based SSL algorithms and traditional supervised learning algorithms (e.g., support vector machines) for multispectral image classification. This research shows that SSL algorithms generally outperform supervised learning algorithms in both classification accuracy and anti-noise ability. In the experiments carried out on two data sets (hyperspectral image and Landsat image), the mean overall accuracies (OAs) of supervised learning algorithms are 15 percent and 86 percent, while the mean OAS of SSL algorithms are 26 percent and 99 percent. To overcome the polynomial complexity of SSL algorithms, we also developed a linear-complexity algorithm by employing multivariate Taylor Series Expansion (TSE) and Woodbury Formula.

Measuring the Influence of Observations in HMMs Through the Kullback–Leibler Distance

We measure the influence of individual observations on the sequence of the hidden states of the Hidden Markov Model (HMM) by means of the Kullback-Leibler distance (KLD). Namely, we consider the KLD between the conditional distribution of the hidden states' chain given the complete sequence of observations and the conditional distribution of the hidden chain given all the observations but the one under consideration. We introduce a linear complexity algorithm for computing the influence of all the observations. As an illustration, we investigate the application of our algorithm to the problem of detecting outliers in HMM data series.

An algorithm of linear complexity for the diagnosis of discrete event systems

This paper concerns fault detection and diagnosis for discrete event systems modeled with partially observed Petri nets. The proposed method provides a decision 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 return on-line diagnosis decisions.

Comparison of type-based and alias-based component recognition for embedded systems software

Component-based software engineering has found broad acceptance within the embedded systems community over the last years. However, to fully exploit its potential in terms of reusability and cost-efficiency, existing code-bases have to be refactored in a component-based way. To support refactorization, static analysis techniques can be used to identify components within coarse-grained layered or even monolithic legacy software for embedded systems. We present an approach for semi-automatic extraction of components from automotive software and compare two different versions, one type-based component-recognition analysis of linear complexity with a more precise version based on a points-to analysis of almost linear algorithmic complexity. Both analyses are applied to an industrial implementation of an automotive communication stack. Each analysis is evaluated with two sets of additional manually created annotations of distinct size and precision. Thus, both analyses are fully evaluated in terms of execution-time, memory consumption and analysis precision, and its impact on the number of recognized components. We show that the analysis with higher precision allows the use of a smaller user-provided filter set and obtain a proper component recognition.

Discrete Elastic Inner Vector Spaces with Application to Time Series and Sequence Mining

This paper proposes a framework dedicated to the construction of what we call discrete elastic inner product allowing one to embed sets of non-uniformly sampled multivariate time series or sequences of varying lengths into inner product space structures. This framework is based on a recursive definition that covers the case of multiple embedded time elastic dimensions. We prove that such inner products exist in our general framework and show how a simple instance of this inner product class operates on some prospective applications, while generalizing the Euclidean inner product. Classification experimentations on time series and symbolic sequences datasets demonstrate the benefits that we can expect by embedding time series or sequences into elastic inner spaces rather than into classical Euclidean spaces. These experiments show good accuracy when compared to the euclidean distance or even dynamic programming algorithms while maintaining a linear algorithmic complexity at exploitation stage, although a quadratic indexing phase beforehand is required.

Resource Selection Algorithms for Economic Scheduling in Distributed Systems

In this paper, we present slot selection algorithms in economic models for independent job batch scheduling in distributed computing with non-dedicated resources. Existing approaches towards resource co-allocation and multiprocessor job scheduling in economic models of distributed computing are based on search of time-slots in resource occupancy schedules. The sought time-slots must match requirements of necessary span, computational resource properties, and cost. Usually such scheduling methods consider only one suited variant of time-slot set. This paper discloses a scheduling scheme that features multi-variant search. Two algorithms of linear complexity for search of alternative variants are compared. Having several optional resource configurations for each job makes an opportunity to perform an optimization of execution of the whole batch of jobs and to increase overall efficiency of scheduling.

Reliability Measurement and Enhancement of the Communication Networks

of ICT (Information and Communication Technology) or the computer communication using electronic messaging has increased tremendously in recent years. Also the modern networks that support ICT are robust, i.e., its failure due to links, routing protocols, congestion etc is rare and as a result, the estimation of the overall reliability of the communication networks, which is #P- complete problem, is very important. This paper presents two linear time complexity algorithms for approximate assessment and the enhancement of the reliability of the given networks. The proposed techniques basically identify the node-pairs having lower reliability, insert communication links in them and calculate the increase in reliability on insertion iteratively until the satisfactory reliability is achieved. The simulated experimentation of the proposed algorithms have been done and compared with the existing methods, which show satisfactory performance.

Algorithms for connected component labeling based on quadtrees

AbstractAn algorithm of linear time complexity is presented to label connected components of a binary image by a quadtree. For a given node, the search for all adjacent nodes is carried out in O(1) (i.e., constant time complexity for the worst case) using our formerly presented algorithm in (Aizawa et al., 3rd International Symposium on Communications, Control, and Signal Processing,2008, 505–510), whereas it explores all possible adjacencies for each node in a usual way. Then during the process of tree formulation in the search, all equivalent relations of labels are stored as lists. Time complexity of the algorithm is O(B+W) for the worst case and its auxiliary space is no more than O(B), where B and W correspond to the number of leaf nodes in a quadtree representing black and white quadrants, respectively. Empirical tests of the algorithm are employed in comparison with another linear time connected component labeling algorithm based on top‐down quadtree traversal algorithm (Samet, IEEE Trans Pattern Anal Mach Intell PAMI‐7 (1985), 94–98), as well as traditional row‐by‐row scanning algorithm using linear time Union‐Find (Fiorio and Gustedt, Theor Comput Sci 154 (1996), 165–181). Our algorithm has shown the best performance in large images. © 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 158–166, 2009.

Probabilistic model of the algorithms of distributed control protocol in the internet network

Consideration was given to a queuing system that models interaction of two basic algorithms of the TCP protocol. Within the framework of analysis of this system, semi-Markov process of the unified data transmission rate was constructed, recurrent analytical representation of the stationary distribution of a Markov chain embedded in this process was determined, and stationary distribution of the original semi-Markov process was obtained. In view of high complexity of the analytical representation of the stationary distribution, an exact numerical linear-complexity algorithm was constructed enabling one to calculate some important characteristics of the initial protocol.

A Recovery Algorithm of Linear Complexity in the Time-Domain Layered Finite Element Reduction Recovery (LAFE-RR) Method for Large-Scale Electromagnetic Analysis of High-Speed ICs

Time-domain layered finite element reduction recovery (LAFE-RR) method was recently developed for large-scale electromagnetic analysis of high-speed integrated circuits (ICs). This method is capable of analytically and rigorously reducing the system matrix of a 3-D multilayer circuit to that of a single-layer one regardless of the original problem size. In addition, the reduced system matrix preserves the sparsity of the original system matrix. In this paper, an efficient algorithm is proposed to recover the volume unknowns in the time-domain LAFE-RR method. This algorithm constitutes a direct solution of the matrix formed by volume unknowns in each layer. This direct solution possesses a linear complexity in both central processing unit (CPU) time and memory consumption. The cost of matrix inversion is negligible. The cost of matrix solution scales linearly with the matrix size. Numerical and experimental results have demonstrated the accuracy and efficiency of the proposed algorithm.

A linear complexity algorithm for the automatic generation of convex multiple input multiple output instructions

The instruction-set extensions problem has been one of the major topics in recent years and it consists of the addition of a set of new complex instructions to a given instruction-set. This problem in its general formulation requires an exhaustive search of the design space to identify the candidate instructions. This search turns into an exponential complexity of the solution. In this paper we propose an efficient linear complexity algorithm for the automatic generation of convex multiple input multiple output instructions, whose convexity is theoretically guaranteed. The proposed approach is not restricted to basic-block level and does not impose limitations either on the number of input and/or output, or on the number of new instructions generated. Our results show a significant overall application speedup (up to ×2.9 for ADPCM decoder) considering the linear complexity of the proposed solution and which therefore compares well with other state-of-art algorithms for automatic instruction-set extensions.

An algorithm for k-error joint linear complexity of binary multisequences

Our aim is to find some of the analogues of results related to k-error linear complexity of single sequences to the case of multisequences over GF(2). This paper presents algorithms for finding the joint linear complexity and the k-error joint linear complexity of m-fold binary multisequences of period 2 n .

Efficient complete and incomplete path openings and closings

Path openings and closings are algebraic morphological operators using families of thin and oriented structuring elements that are not necessarily perfectly straight. These operators can typically be used in filtering applications in lieu of operators based on the more standard families of straight line structuring elements. They yield results which are less constrained than filters based on straight line segments, yet more constrained than connected area or other attribute-based operators. Furthermore, path operators can be parametrised to behave more like either extreme. Natural implementations of this idea using actual suprema or infima of morphological operators with paths as structuring elements would imply exponential complexity. Fortunately, a linear complexity algorithm exists in the literature. This algorithm has similar running times as the best known implementation of morphological operators using straight lines as structuring elements. However, even this implementation is sometimes not fast enough, leading practitioners to favour some attribute-based operators instead, which in some applications is not the best solution. In this paper, we propose an implementation of path-based morphological operators that is shown experimentally to exhibit a logarithmic complexity and comparable computing times with those of attribute-based operators. This implementation has the added benefit of allowing the computation of the related opening transform at no extra computational cost. In order to give additional flexibility and noise-robustness to these operators, we also investigate the case when some pixels are left ignored from the path (i.e. “jumps” are allowed) and form incomplete paths.

Time-domain analysis methodology for large-scale RLC circuits and its applications

With soaring work frequency and decreasing feature sizes, VLSI circuits with RLC parasitic components are more like analog circuits and should be carefully analyzed in physical design. However, the number of extracted RLC components is typically too large to be analyzed efficiently by using present analog circuit simulators like SPICE. In order to speedup the simulations without error penalty, this paper proposes a novel methodology to compress the time-descritized circuits resulted from numerical integration approximation at every time step. The main contribution of the methodology is the efficient structure-level compression of DC circuits containing many current sources, which is an important complement to present circuit analysis theory. The methodology consists of the following parts: 1) An approach is proposed to delete all intermediate nodes of RL branches. 2) An efficient approach is proposed to compress and back-solve parallel and serial branches so that it is error-free and of linear complexity to analyze circuits of tree topology. 3) The Y to π transformation method is used to error-free reduce and back-solve the intermediate nodes of ladder circuits with the linear complexity. Thus, the whole simulation method is very accurate and of linear complexity to analyze circuits of chain topology. Based on the methodology, we propose several novel algorithms for efficiently solving RLC-model transient power/ground (P/G) networks. Among them, EQU-ADI algorithm of linear-complexity is proposed to solve RLC P/G networks with mesh-tree or mesh-chain topologies. Experimental results show that the proposed method is at least two orders of magnitude faster than SPICE while it can scale linearly in both time-and memory-complexity to solve very large P/G networks.

Bi-iterative least-square method for subspace tracking

Subspace tracking is an adaptive signal processing technique useful for a variety of applications. In this paper, we introduce a simple bi-iterative least-square (Bi-LS) method, which is in contrast to the bi-iterative singular value decomposition (Bi-SVD) method. We show that for subspace tracking, the Bi-LS method is easier to simplify than the Bi-SVD method. The linear complexity algorithms based on Bi-LS are computationally more efficient than the existing linear complexity algorithms based on Bi-SVD, although both have the same performance for subspace tracking. A number of other existing subspace tracking algorithms of similar complexity are also compared with the Bi-LS algorithms.

Video shot characterization

This paper presents a practical approach to detecting shot cuts and extracting keyframes from video sequences. Shot cut detection has two stages - global motion compensation, followed by an adaptive thresholding algorithm. The motion information is further utilized to extract representative keyframes. Special consideration has been given to achieving real-time performance on a regular PC, which led to a motion estimation algorithm of linear complexity.

A shape preserving representation with an evaluation algorithm of linear complexity

We consider a blending basis for which we obtain an algorithm for the evaluation of polynomial curves with linear time complexity and we prove that it is a normalized totally positive basis. Therefore, it simultaneously satisfies efficiency and shape preservation. We also provide the corner cutting algorithm for obtaining the Bézier polygon from the control polygon with respect this basis. Related bases with additional properties are also considered.