For a fixed pattern graph H, let H-CONTRACTIBILITY denote the problem of deciding whether a given input graph is contractible to H. This paper is part I of our study on the computational complexity of the H-CONTRACTIB...
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For a fixed pattern graph H, let H-CONTRACTIBILITY denote the problem of deciding whether a given input graph is contractible to H. This paper is part I of our study on the computational complexity of the H-CONTRACTIBILITY problem. We continue a line of research that was started in 1987 by Brouwer and Veldman, and we determine the computational complexity of the H-CONTRACTIBILITY problem for certain classes of pattern graphs. In particular, we pinpoint the complexity for all graphs H with five vertices except for two graphs, whose polynomial time algorithms are presented in part II. Interestingly, in all connected cases that are known to be polynomially solvable, the pattern graph H has a dominating vertex, whereas in all cases that are known to be NP-complete, the pattern graph H does not have a dominating vertex. (C) 2007 Wiley Periodicals, Inc.
Spinal codes, a new class of rateless codes, have received considerable attention for their capacity-approaching performance over noisy channels. Hash function is the core of a spinal encoder to generate infinite code...
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Spinal codes, a new class of rateless codes, have received considerable attention for their capacity-approaching performance over noisy channels. Hash function is the core of a spinal encoder to generate infinite coded symbols, which has higher hardware complexity. In this study, the authors propose a multiplicative repetition-based method instead of the hash function to generate innumerable symbols with low encoding complexity. Furthermore, both frozen-aided and cyclic redundancy check-aided decoding methods are proposed to improve the spectral efficiency. Simulation results show that the proposed spinal codes have lower computational complexity and can achieve higher spectral efficiency in the high signal-to-noise ratio region compared with the conventional ones over both additive white Gaussian noise and Rayleigh fading channels.
The spectrum of a first-order sentence is the set of cardinalities of its finite models. We refine the well-known equality between the class of spectra and the class of sets (of positive integers) accepted by nondeter...
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The spectrum of a first-order sentence is the set of cardinalities of its finite models. We refine the well-known equality between the class of spectra and the class of sets (of positive integers) accepted by nondeterministic Turing machines in polynomial time. Let Sp(d∀)Sp(d∀) denote the class of spectra of sentences with d universal quantifiers. For any integer
first-order sentences
spectrum
generalized spectrum
computational complexity
non-deterministic Turing machine
In simulation-based realization of complex systems, we are forced to address the issue of computational complexity. One critical issue that must be addressed is the approximation of reality using surrogate models to r...
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In simulation-based realization of complex systems, we are forced to address the issue of computational complexity. One critical issue that must be addressed is the approximation of reality using surrogate models to replace expensive simulation models of engineering problems. In this paper, we critically review over 200 papers. We find that a framework for selecting appropriate surrogate modeling methods for a given function with specific requirements has been lacking. Having such a framework for surrogate model users, specifically practitioners in industry, is very important because there is very limited information about the performance of different models before applying them on the problem. Our contribution in this paper is to address this gap by creating practical guidance based on a trade-off among three main drivers, namely, size (how much information is necessary to compute the surrogate model), accuracy (how accurate the surrogate model must be) and computational time (how much time is required for the surrogate modeling process). Using the proposed guidance a huge amount of time is saved by avoiding time-consuming comparisons before selecting the appropriate surrogate model. To make this contribution, we review the state-of-the-art surrogate modeling literature to answer the following three questions: (1) What are the main classes of the design of experiment (DOE) methods, surrogate modeling methods and model-fitting methods based on the requirements of size, computational time, and accuracy? (2) Which surrogate modeling method is suitable based on the critical characteristics of the requirements of size, computational time and accuracy? (3) Which DOE is suitable based on the critical characteristics of the requirements of size, computational time and accuracy? Based on these three characteristics, we find six different qualitative categories for the surrogate models through a critical evaluation of the literature. These categories provide a framework for
The state-of-the-art graph searching algorithm applied to the optimal global path planning problem for mobile robots is the A* algorithm with the heap structured open list. In this paper, we present a novel algorithm,...
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The state-of-the-art graph searching algorithm applied to the optimal global path planning problem for mobile robots is the A* algorithm with the heap structured open list. In this paper, we present a novel algorithm, called the L* algorithm, which can be applied to global path planning and is faster than the A* algorithm. The structure of the open list with the use of bidirectional sublists (buckets) ensures the linear computational complexity of the L* algorithm because the nodes in the current bucket can be processed in any sequence and it is not necessary to sort the bucket. Our approach can maintain the optimality and linear computational complexity with the use of the cost expressed by floating-point numbers. The paper presents the requirements of the L* algorithm use and the proof of the admissibility of this algorithm. The experiments confirmed that the L* algorithm is faster than the A* algorithm in various path planning scenarios. We also introduced a method of estimating the execution time of the A* and the L* algorithm. The method was compared with the experimental results.
The practicality of robust model predictive control of systems with model uncertainties depends on the time consumed for solving a defined optimization problem. This paper presents a method for the computational compl...
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The practicality of robust model predictive control of systems with model uncertainties depends on the time consumed for solving a defined optimization problem. This paper presents a method for the computational complexity reduction in a robust model predictive control. First a scaled state vector is defined such that the objective function contours in the defined optimization problem become vertical or horizontal ellipses or circles, and then the control input is determined at each sampling time as a state feedback that minimizes the infinite horizon objective function by solving some linear matrix inequalities. The simulation results show that the number of iterations to solve the problem at each sampling interval is reduced while the control performance does not alter noticeably. (C) 2014 ISA. Published by Elsevier Ltd. All rights reserved.
The concept of flexibility - originated in the context of heat exchanger networks design - is associated with a substructure which allows the same optimal value on the substructure (for example an optimal flow) as in ...
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The concept of flexibility - originated in the context of heat exchanger networks design - is associated with a substructure which allows the same optimal value on the substructure (for example an optimal flow) as in the whole structure, for all the costs in a given range of costs. In this work, we extend the concept of flexibility to general combinatorial optimization problems, and prove several computational complexity results in this new framework. Under some monotonicity conditions, we prove that a combinatorial optimization problem can be polynomially reduced to its associated flexibility problem. However, the minimum cut, maximum weighted matching and shortest path problems have NP-complete associated flexibility problems. In order to obtain polynomial flexibility problems, we have to restrict ourselves to combinatorial optimization problems on matroids.
This paper presents a syntax of approximate formulae suited for the logic with counting quantifiers SOLP. This logic was formalised by us in [1] where, among other properties, we showed the following facts: (i) In the...
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This paper presents a syntax of approximate formulae suited for the logic with counting quantifiers SOLP. This logic was formalised by us in [1] where, among other properties, we showed the following facts: (i) In the presence of a built-in (linear) order, SOLP can describe NP-complete problems and some of its fragments capture the classes P and NL;(ii) weakening the ordering relation to an almost order we can separate meaningful fragments, using a combinatorial tool adapted to these languages. The purpose of our approximate formulae is to provide a syntactic approximation to the logic SOLP, enhanced with a built-in order, that should be complementary of the semantic approximation based on almost orders, by means of producing logics where problems are syntactically described within a small counting error. We introduce a concept of strong expressibility based on approximate formulae, and show that for many fragments of SOLP with built-in order, including ones that capture P and NL, expressibility and strong expressibility are equivalent. We state and prove a Bridge Theorem that links expressibility in fragments of SOLP over almost-ordered structures to strong expressibility with respect to approximate formulae for the corresponding fragments over ordered structures. A consequence of these results is that proving inexpressibility over fragments of SOLP with built-in order could be done by proving inexpressibility over the corresponding fragments with built-in almost order, where separation proofs are allegedly easier.
The broad application area and accompanying challenges make machine learning-based recognition of handwritten scripts a demanding field. Individuals' writing practices and inherent variations in the size, shape, a...
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The broad application area and accompanying challenges make machine learning-based recognition of handwritten scripts a demanding field. Individuals' writing practices and inherent variations in the size, shape, and tilt of characters may increase the difficulty level. Deep convolutional neural network (DCNN) models have been successful in solving pattern recognition problems, but at the expense of a considerable number of trainable parameters and heavy computational loads. The proposed work addresses these problems by using the shifted window (SWIN) transformer method to recognize handwritten Devanagari numerals for the first time. In the presented model, the SWIN transformer is finely tuned to withstand popular DCNN models, such as VGG-16Net, ResNet-50, and DenseNet-121, in terms of recognition accuracy, space requirement, and computational complexity. The model successfully attained a recognition accuracy of 99.20% with only 0.218 million trainable parameters and 0.0912 giga floating-point operations per second (FLOPs). This indicates the validity and soundness of the proposed model for recognizing handwritten Devanagari numerals.
LHE (logarithmical hopping encoding) is a computationally efficient image compression algorithm that exploits the Weber-Fechner law to encode the error between colour component predictions and the actual value of such...
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LHE (logarithmical hopping encoding) is a computationally efficient image compression algorithm that exploits the Weber-Fechner law to encode the error between colour component predictions and the actual value of such components. More concretely, for each pixel, luminance and chrominance predictions are calculated as a function of the surrounding pixels and then the error between the predictions and the actual values are logarithmically quantised. The main advantage of LHE is that although it is capable of achieving a low-bit rate encoding with high quality results in terms of peak signal-to-noise ratio (PSNR) and image quality metrics with full-reference (FSIM) and non-reference (blind/referenceless image spatial quality evaluator), its time complexity is O(n) and its memory complexity is O(1). Furthermore, an enhanced version of the algorithm is proposed, where the output codes provided by the logarithmical quantiser are used in a pre-processing stage to estimate the perceptual relevance of the image blocks. This allows the algorithm to downsample the blocks with low perceptual relevance, thus improving the compression rate. The performance of LHE is especially remarkable when the bit per pixel rate is low, showing much better quality, in terms of PSNR and FSIM, than JPEG and slightly lower quality than JPEG-2000 but being more computationally efficient.
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