Experimental results based on offline processing reported at optical conferences increasingly rely on neural network-based equalizers for accurate data recovery. However, achieving low-complexity implementations that ...
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computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitiv...
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A Roman{2}-dominating function of a graph G = (V, E) is a function f : V ? {0, 1, 2} such that every vertex x ? V with f (x) = 0 either there exists at least one vertex y ? N(x) with f (y) = 2 or there are at least tw...
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A Roman{2}-dominating function of a graph G = (V, E) is a function f : V ? {0, 1, 2} such that every vertex x ? V with f (x) = 0 either there exists at least one vertex y ? N(x) with f (y) = 2 or there are at least two vertices u, v ? N(x) with f (u) = f (v) = 1. The weight of a Roman{2}-dominating function f on G is defined to be the value of S-x?V f (x). The minimum weight of a Roman{2}-dominating function on G is called the Roman{2}-domination number of G. In this paper, we prove that the decision problem associated with Roman{2}-domination number is N P-complete even when restricted to subgraphs of grid graphs. Additionally, we answer an open question about the approximation hardness of Roman{2}-domination problem for bounded degree graphs.
Many important problems in AI, among them #SAT, parameter learning and probabilistic inference go beyond the classical satisfiability problem. Here, instead of finding a solution we are interested in a quantity associ...
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Many important problems in AI, among them #SAT, parameter learning and probabilistic inference go beyond the classical satisfiability problem. Here, instead of finding a solution we are interested in a quantity associated with the set of solutions, such as the number of solutions, the optimal solution or the probability that a query holds in a solution. To model such quantitative problems in a uniform manner, a number of frameworks, e.g. Algebraic Model Counting and Semiring-based Constraint Satisfaction Problems, employ what we call the semiring paradigm. In the latter the abstract algebraic structure of the semiring serves as a means of parameterizing the problem definition, thus allowing for different modes of quantitative computations by choosing different semirings. While efficiently solvable cases have been widely studied, a systematic study of the computational complexity of such problems depending on the semiring parameter is missing. In this work, we characterize the latter by NP(R), a novel generalization of NP over semiring R, and obtain NP(R)-completeness results for a selection of semiring frameworks. To obtain more tangible insights into the hardness of NP(R), we link it to well-known complexity classes from the literature. Interestingly, we manage to connect the computational hardness to properties of the semiring. Using this insight, we see that, on the one hand, NP(R) is always at least as hard as NP or MoDpP depending on the semiring R and in general unlikely to be in FPSPACE(PoLY). On the other hand, for broad subclasses of semirings relevant in practice we can employ reductions to NP, MoDpP and #P. These results show that in many cases solutions are only mildly harder to compute than functions in NP, MoDpP and #P, give us new insights into how problems that involve counting on semirings can be approached, and provide a means of assessing whether an algorithm is appropriate for a given class of problems.
Hexagonal grid layouts are advantageous in microarray technology;however, hexagonal grids appear in many fields, especially given the rise of new nanostructures and metamaterials, leading to the need for image analysi...
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Hexagonal grid layouts are advantageous in microarray technology;however, hexagonal grids appear in many fields, especially given the rise of new nanostructures and metamaterials, leading to the need for image analysis on such structures. This work proposes a shock-filter-based approach driven by mathematical morphology for the segmentation of image objects disposed in a hexagonal grid. The original image is decomposed into a pair of rectangular grids, such that their superposition generates the initial image. Within each rectangular grid, the shock-filters are once again used to confine the foreground information for each image object into an area of interest. The proposed methodology was successfully applied for microarray spot segmentation, whereas its character of generality is underlined by the segmentation results obtained for two other types of hexagonal grid layouts. Considering the segmentation accuracy through specific quality measures for microarray images, such as the mean absolute error and the coefficient of variation, high correlations of our computed spot intensity features with the annotated reference values were found, indicating the reliability of the proposed approach. Moreover, taking into account that the shock-filter PDE formalism is targeting the one-dimensional luminance profile function, the computational complexity to determine the grid is minimized. The order of growth for the computational complexity of our approach is at least one order of magnitude lower when compared with state-of-the-art microarray segmentation approaches, ranging from classical to machine learning ones.
Increasing the penetration of variable and uncertain renewables and electric vehicles in power systems may give rise to problems (such as network congestion and commitment mismatches) if not controlled strategically. ...
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Increasing the penetration of variable and uncertain renewables and electric vehicles in power systems may give rise to problems (such as network congestion and commitment mismatches) if not controlled strategically. This demands control solutions in the form of energy management strategies for active distribution networks which would control the connected distributed energy resources and storage units in real-time to address the mentioned challenges. Centralized strategies may fail to serve this purpose for large-scale distribution networks due to their inherent shortcomings like vulnerability to single point of failures and large computing times. Unlike centralized approaches, decentralized control strategies show more potential. This paper presents one such solution, based on an adaptive multi-agent system, to control a large-scale distribution network in real-time. Its performance is compared with the results obtained with the corresponding centralized optimization problem, modeled as a mixed integer linear programming problem. Both the centralized version and the decentralized multi-agent version of the problem under consideration are presented and a case study is designed for the comparison. The comparison shows that the designed multi-agent system produces a near-optimal solution in real-time while the centralized optimization strategy struggles in terms of computational complexities for larger distribution networks.(c) 2017 Elsevier Inc. All rights reserved.
The paper focuses on analysing the computational time complexity of Frontal Cellular Automata (FCAs) and comparing it with Classic Cellular Automata (CCAs). Some variants of CCAs and FCAs are described and presented b...
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The paper focuses on analysing the computational time complexity of Frontal Cellular Automata (FCAs) and comparing it with Classic Cellular Automata (CCAs). Some variants of CCAs and FCAs are described and presented by showing differences in their structure and transition rules. Several variants of simple two-dimensional (2D) CAs and four variants of three-dimensional (3D) CAs for grain growth have been developed, tested and analysed. These four 3D CA algorithms are described. The calculation time of several simulation cases is measured for 2D and 3D CAs. The computational time complexity is determined on the basis of these measurements. The paper also takes into account the parallelisation of calculations with CAs. Time measurements show the possibility of accelerating the calculations. The paper also presents examples of the application of FCAs to solidification, recrystallisation, phase transformation and grain refinement with giving their simulation time. The computational complexity of different CAs is discussed, and FCAs with cells organised into linked lists show the lowest computational complexity. The paper ends with conclusions highlighting the low computational complexity and time efficiency of FCA.
In this paper we study the computational complexity of computing an evolutionary stable strategy (ESS) in multi-player symmetric games. For two-player games, deciding existence of an ESS is complete for Σ2p, the seco...
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Distribution system state estimation (DSSE) is a key monitoring function for system operators to automate, control, and operate the active distribution grids. The computational complexity of the DSSE algorithm is a de...
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Distribution system state estimation (DSSE) is a key monitoring function for system operators to automate, control, and operate the active distribution grids. The computational complexity of the DSSE algorithm is a design factor for implementing a real-time monitoring system. As a common criterion, the elapsed time has been used in many works to determine whether a developed DSSE solver, regardless of data acquisition and bad data detection steps, can satisfy the requirement of real-time operation. This measure, however, is machine-dependent and thus may not be a good indicator to show the computational burden of a state estimation method in run-time. This article proposes instead to use floating point operation (FLOP) which is a machine-independent computational complexity measure. The number of FLOPs is a suitable relative performance indicator in determining how fast a method could be executed. In this article, the computational cost of different DSSE algorithms is mathematically derived in terms of FLOPs. On this basis, this article shows that FLOP is a better measure than the more commonly used elapsed time for making design decisions about the choice of the DSSE method based on computational complexity.
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