A graph is well-indumatched if all its maximal induced matchings are of the same size. We first prove that recognizing whether a graph is well-indumatched is a co-NP-complete problem even for (2P(5), K-1,K-5)-free gra...
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A graph is well-indumatched if all its maximal induced matchings are of the same size. We first prove that recognizing whether a graph is well-indumatched is a co-NP-complete problem even for (2P(5), K-1,K-5)-free graphs. We then show that decision problems INDEPENDENT DOMINATING SET, INDEPENDENT SET, and DOMINATING SET are NP-complete for the class of well-indumatched graphs. We also show that this class is a co-indumatching hereditary class, i.e., it is closed under deleting the end-vertices of an induced matching along with their neighborhoods, and we characterize well-indumatched graphs in terms of forbidden co-indumatching subgraphs. We prove that recognizing a co-indumatching subgraph is an NP-complete problem. We introduce a perfectly well-indumatched graph, in which every induced subgraph is well-indumatched, and characterize the class of these graphs in terms of forbidden induced subgraphs. Finally, we show that the weighted versions of problems INDEPENDENT DOMINATING SET and INDEPENDENT SET can be solved in polynomial time for perfectly well-indumatched graphs, but problem DOMINATING SET is NP-complete. (C) 2016 Elsevier B.V. All rights reserved.
Analysis/synthesis systems designed for low bit rate image coding, their impact on overall system quality, and their computational complexity are discussed. The investigation focuses on the design of analysis/synthesi...
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Analysis/synthesis systems designed for low bit rate image coding, their impact on overall system quality, and their computational complexity are discussed. The investigation focuses on the design of analysis/synthesis systems for image coding and the perceptual impact of these systems at low bit rates. Two objectives are emphasized in developing these systems: confining the total size of the subband images to be equal to the original image size, and designing the filters so that perceptual distortion is not introduced by the analysis/synthesis system. Methods based on circular convolution and symmetric extensions are developed and discussed in detail. The theory, design, and implementation of both recursive and nonrecursive filtering systems are discussed. Methods are introduced which display advantages over conventional quadrature mirror filter based approaches.< >
In this paper, we study unbounded parallel-batch scheduling with drop-line tasks to minimize a regular objective function, where by drop-line tasks we mean that the completion time of each task (job) is equal to the s...
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In this paper, we study unbounded parallel-batch scheduling with drop-line tasks to minimize a regular objective function, where by drop-line tasks we mean that the completion time of each task (job) is equal to the sum of the starting time of the batch containing the task and the processing time of the task. In the problems considered in this paper, we assume that the tasks have individual release dates and the general regular objective function to be minimized is either of the sum-form or of the max-form. We then study the computational complexity of these problems on an unbounded parallel-batch processor. We show that (i) the problems are binary NP-hard and are solvable in pseudo-polynomial times, and (ii) when the number of processing times or release dates is a constant, the problems are solvable in polynomial times. We also point out some consequences of approximation algorithms.
This study proposes some multivariable approaches for power allocation in orthogonal frequency multiple access-based differential chaos shift keying (OFDM-DCSK) system. The objective is to minimise the overall bit err...
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This study proposes some multivariable approaches for power allocation in orthogonal frequency multiple access-based differential chaos shift keying (OFDM-DCSK) system. The objective is to minimise the overall bit error rate (BER) under the total transmission power limit. There is some literature focusing on the power allocation for OFDM-DCSK systems, but all of them have only addressed the case where the power allocated to the reference subcarrier is assumed to be equal to one to simplify the problem to a single-variable optimisation problem. In this study, the authors simultaneously take the reference and data-bearing subcarriers power into consideration. They formulate a multivariable optimisation problem and solve it using Lagrange relaxation to derive a closed form solution. As the main contribution, the problem is converted to a cubic equation which is solved theoretically. Since the equation is non-convex, they solve it again using a genetic algorithm (GA)-based method for additive white Gaussian noise channel as a case study. The heuristic algorithm validates the theoretical approach. As another conclusion, the simulation results indicate that both of the proposed approaches outperform algorithms relaxing the reference power in terms of the BER performance, but the analytical solution leads to less time complexity in comparison with the GA-based method.
In this paper, we investigate joint user (UE) scheduling, base station (BS) clustering and beamforming design in a dense network. To reduce the computation burden, we propose a deep unfolding UE scheduling, BS cluster...
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In this paper, we investigate joint user (UE) scheduling, base station (BS) clustering and beamforming design in a dense network. To reduce the computation burden, we propose a deep unfolding UE scheduling, BS clustering and beamforming (DU-USBCB) method based on the iterative weighted minimum mean square error (WMMSE) algorithm, where the UE scheduling and BS clustering are represented by the group sparsity of the transmit beamforming vectors. The proposed DU-USBCB neural network layer comprises receive coefficient, weight and transmit beamforming vector modules, the former two of which have closed-form expressions. For the third module, the group sparse transmit beamforming vectors are obtained by multiple steps of projected gradient descent and nonlinear sparsification, where the step-sizes are learned through unsupervised learning. We also propose a distributed UE selection (DUS) algorithm, which helps reduce the computation workload. Simulation results verify the effectiveness of the proposed DU-USBCB and DUS methods. The learned step-sizes are directly applied in the testing scenarios with different numbers of UEs, BSs and antennas as well as incomplete channel state information. Besides, our proposed methods can achieve comparable performance but with about 53% and 89% computation reduction compared to the RSRP-WMMSE and SWMMSE methods respectively.
High computational complexity and inadequate parallelism have deterred the use of subspace-based algorithms in real-time systems, Recently, we proposed a new class of fast subspace tracking (FST) algorithms that overc...
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High computational complexity and inadequate parallelism have deterred the use of subspace-based algorithms in real-time systems, Recently, we proposed a new class of fast subspace tracking (FST) algorithms that overcome these problems by exploiting the matrix structure inherent in multisensor processing, These algorithms simultaneously track an orthonormal basis for the signal subspace and preserve signal eigenstructure information while requiring only O(Nr) operations per update (where N is the number of channels, and r is the effective rank), Because of their low computational complexity, these algorithms have applications in both recursive and block data processing, Because they preserve the signal eigenstructure as well as compute an orthonormal basis for the signal subspace, these algorithms may be used in a wide range of sensor array applications including bearing estimation, beamforming, and recursive least squares, In this paper, we will present a detailed description of the FST algorithm and its rank adaptive variation (RA-FST) as well as recent enhancements, We also demonstrate FST's rapid convergence properties in a number of application scenarios.
This paper concerns the hardness of approximating the closest vector in a lattice with preprocessing in l1norm,and gives a polynomial time algorithm for GapCVPPγin l1norm with gapγ=O(n/log n).The gap is smaller than...
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This paper concerns the hardness of approximating the closest vector in a lattice with preprocessing in l1norm,and gives a polynomial time algorithm for GapCVPPγin l1norm with gapγ=O(n/log n).The gap is smaller than that obtained by simply generalizing the approach given by Aharonov and *** main technical ingredient used in this paper is the discrete Laplace distribution on lattices which may be of independent interest.
Aiming at minimizing the transmit power of orthogonal frequency-division multiplexing (OFDM) systems subject to the target data rate, the target bit error rate (BER), the maximum allowable power per subcarrier, and th...
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Aiming at minimizing the transmit power of orthogonal frequency-division multiplexing (OFDM) systems subject to the target data rate, the target bit error rate (BER), the maximum allowable power per subcarrier, and the-maximum allowable size of constellations, we present a couple of new discrete bitloading algorithms, named efficient bit filling (EBF) and efficient bit removal (EBR), which are based on our new idea of group-by-group bit filling. Both EBF and EBR perform bit loading in two stages and are able to converge to the optimal bit-allocation profile. In the first stage, an intermediate bit-allocation profile, which is tightly close to the final bit-allocation profile, is obtained by using our proposed group-by-group bit filling (for EBF) or group-by-group bit removal (for EBR). In the second stage, the well-known greedy bit filling (for EBF) or greedy bit removal (for EBR) is performed for the remaining bits (usually of a small size). Analytical and numerical results reveal that the proposed algorithms converge to the optimal bit allocation with much lower computational complexities than existing optimal algorithms. It is also shown that the proposed algorithms outperform typical suboptimal algorithms in power efficiency with relatively higher computational complexities.
Recently, the improved simple set-membership affine projection (IS-SM-AP) algorithm has been proposed in order to exploit sparsity in system models. Although its update equation resembles that of the set-membership af...
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Recently, the improved simple set-membership affine projection (IS-SM-AP) algorithm has been proposed in order to exploit sparsity in system models. Although its update equation resembles that of the set-membership affine projection (SM-AP) algorithm, the IS-SM-AP algorithm has two fundamental advantages over the SM-AP algorithm: (i) it can exploit sparsity in system models and (ii) its computational complexity is lower. Up to now, the properties of this algorithm have been addressed only through numerical simulations, and no analytical study has been presented. To fill this gap, in this study, the authors analyse the steady-state mean squared error of the IS-SM-AP algorithm using the energy conservation method. Furthermore, some important implementation issues are addressed, and a time-varying parameter for the discard function is proposed. Finally, the authors present numerical results corroborating the theoretical analysis and the effectiveness of the proposed time-varying parameter.
Traditional results in subrecursion theory are integrated with the recent work in "predicative recursion" by defining a simple ranking rho of all primitive recursive functions. The hierarchy defined by this ...
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Traditional results in subrecursion theory are integrated with the recent work in "predicative recursion" by defining a simple ranking rho of all primitive recursive functions. The hierarchy defined by this ranking coincides with the Grzegorczyk hierarchy at and above the linear-space level. Thus, the result is like an extension of the Schwichtenberg-Muller theorems. When primitive recursion is replaced by recursion on notation, the same series of classes is obtained except with the polynomial time computable functions at the first level.
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