The Computational Complexity of One-Dimensional Sandpiles

2005 ◽  
pp. 342-348
Author(s):  
Peter Bro Miltersen
Keyword(s):  
Computational Complexity ◽  
One Dimensional

scholarly journals Two-Dimensional Direction-of-Arrivals Estimation Based on One-Dimensional Search Using Rank Deficiency Principle

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Feng-Gang Yan ◽  
Zhi-Kun Chen ◽  
Ming-Jian Sun ◽  
Yi Shen ◽  
Ming Jin
Keyword(s):  
Computational Complexity ◽  
Signal Classification ◽  
Two Dimensional ◽  
Music Algorithm ◽  
Signal Parameter ◽  
Rank Deficiency ◽  
Multiple Signal Classification ◽  
One Dimensional ◽  
Pair Matching ◽  
Improved Accuracy

A novel efficient method for two-dimensional (2D) direction-of-arrivals (DOAs) estimation is proposed to reduce the computational complexity of conventional 2D multiple signal classification (2D-MUSIC) algorithm with uniform rectangular arrays (URAs). By introducing two electrical DOAs, the formula of 2D-MUSIC is transformed into a new one-dimensional (1D) quadratic optimal problem. This 1D quadratic optimal problem is further proved equivalent to finding the conditions of noise subspace rank deficiency (NSRD), which can be solved by an efficient 1D spectral search, leading to a novel NSRD-MUSIC estimator accordingly. Unlike 2D-MUSIC with exhaustive 2D search, the proposed technique requires only an efficient 1D one. Compared with the estimation of signal parameter via rotation invariance techniques (ESPRIT), NSRD-MUSIC has a significantly improved accuracy. Moreover, the new algorithm requires no pair matching. Numerical simulations are conducted to verify the efficiency of the new estimator.

scholarly journals Two Notes on the Computational Complexity of One-Dimensional Sandpiles

1999 ◽  
Vol 6 (3) ◽  
Author(s):  
Peter Bro Miltersen
Keyword(s):  
Computational Complexity ◽  
Upper Bound ◽  
Prediction Problem ◽  
One Dimensional ◽  
The One

We prove that the one-dimensional sandpile prediction problem is<br />in AC1. The previously best known upper bound on the ACi-scale<br />was AC2. We also prove that it is not in AC1−epsilon for any constant<br /> epsilon > 0.

scholarly journals An algorithm for determining the K-best solutions of the one-dimensional Knapsack problem

2000 ◽  
Vol 20 (1) ◽  
pp. 117-134 ◽  
Author(s):  
Horacio Hideki Yanasse ◽  
Nei Yoshihiro Soma ◽  
Nelson Maculan
Keyword(s):  
Computational Complexity ◽  
Knapsack Problem ◽  
One Dimensional ◽  
The One ◽  
With Memory

In this work we present an enumerative scheme for determining the K-best solutions (K > 1) of the one dimensional knapsack problem. If n is the total number of different items and b is the knapsack's capacity, the computational complexity of the proposed scheme is bounded by O(Knb) with memory requirements bounded by O(nb). The algorithm was implemented in a workstation and computational tests for varying values of the parameters were performed.

Inverse Kinematics of Discretely Actuated Ball-Joint Manipulators Using Workspace Density

2015 ◽  
Author(s):  
Hui Dong ◽  
Taosha Fan ◽  
Zhijiang Du ◽  
Gregory Chirikjian
Keyword(s):  
Fourier Transform ◽  
Computational Complexity ◽  
Inverse Kinematics ◽  
Solution Space ◽  
Rotation Group ◽  
Ball Joint ◽  
End Effector ◽  
Numerical Examples ◽  
One Dimensional ◽  
Elegant Form

We present a workspace-density-based (WSDB) method to solve the inverse kinematics of discretely actuated ball-joint manipulators. Intuitively speaking, workspace density measures the flexibility of a robotic manipulator when the end-effector is fixed at a certain pose or position. We use the SE(3) Fourier transform to derive the workspace density for ball-joint manipulators and show that the workspace density has a concise and elegant form. Then we show that the state for each joint is determined by maximizing the workspace density of subsequent sub-manipulators. We demonstrate our method with several numerical examples. In particular, we show that our method can provide a solution that approximately minimizes the deviation of the end-effector and its computational complexity is linear with respect to the number of joints. Hence our method is very efficient in solving the inverse kinematics of redundant discretely actuated ball-joint manipulators. In addition, we prove that the solution space of our method is reduced from the rotation group SO(3) to a one-dimensional interval.

scholarly journals 1D Frequency Transformation- Based Amplitude- Only Images for Copyright- and Privacy- Protection in Image Trading Systems

1970 ◽  
Vol 8 (2) ◽  
pp. 133-144
Author(s):  
Wannida Sae-Tang ◽  
Shenchuan Liu ◽  
Masaaki Fujiyoshi ◽  
Hitoshi Kiya
Keyword(s):  
Computational Complexity ◽  
Privacy Protection ◽  
Linear Scaling ◽  
Two Dimensional ◽  
Digital Fingerprinting ◽  
Trading Systems ◽  
Frequency Transformation ◽  
One Dimensional ◽  
Low Intensity

This paper proposes an effective method of generating amplitude-only images (AOIs) which are inversely transformed amplitude components of images and which are used in the copyright- and privacyprotected digital fingerprinting-based image trading systems. The proposed method applies a one-dimensional frequency transformation to an image for generating the AOI with low intensity range (IR), whereas the IR of the AOI in the conventional method using a two-dimensional transformation is too large to store or transmit. The proposed method is distinct from other IR reduction approaches such as clipping, linear and non-linear scaling, block division, and random sign assignment which require extra-calculations, it reduces the computational complexity while it reduces IRs of AOIs. Moreover, experimental results show that the proposed method enhances the quality of fingerprinted images and fingerprinting performance.

scholarly journals A Novel 1-D CCANet for ECG Classification

2021 ◽  
Vol 11 (6) ◽  
pp. 2758
Author(s):  
Ian-Christopher Tanoh ◽  
Paolo Napoletano
Keyword(s):  
Neural Network ◽  
Computational Complexity ◽  
Convolutional Neural Network ◽  
Frequency Domain ◽  
Time Domain ◽  
Complex Structures ◽  
Autoregressive Modeling ◽  
One Dimensional ◽  
Electrocardiogram Ecg

This paper puts forward a 1-D convolutional neural network (CNN) that exploits a novel analysis of the correlation between the two leads of the noisy electrocardiogram (ECG) to classify heartbeats. The proposed method is one-dimensional, enabling complex structures while maintaining a reasonable computational complexity. It is based on the combination of elementary handcrafted time domain features, frequency domain features through spectrograms and the use of autoregressive modeling. On the MIT-BIH database, a 95.52% overall accuracy is obtained by classifying 15 types, whereas a 95.70% overall accuracy is reached when classifying 7 types from the INCART database.

scholarly journals Low-complexity CNN with 1D and 2D filters for super-resolution

2020 ◽  
Vol 17 (6) ◽  
pp. 2065-2076 ◽  
Author(s):  
Jangsoo Park ◽  
Jongseok Lee ◽  
Donggyu Sim
Keyword(s):  
Computational Complexity ◽  
High Frequency ◽  
Visual Information ◽  
Signal To Noise Ratio ◽  
Super Resolution ◽  
Low Complexity ◽  
One Dimensional ◽  
Front End ◽  
Proposed Model ◽  
Deep Learning Model

Abstract This paper proposes a low-complexity convolutional neural network (CNN) for super-resolution (SR). The proposed deep-learning model for SR has two layers to deal with horizontal, vertical, and diagonal visual information. The front-end layer extracts the horizontal and vertical high-frequency signals using a CNN with one-dimensional (1D) filters. In the high-resolution image-restoration layer, the high-frequency signals in the diagonal directions are processed by additional two-dimensional (2D) filters. The proposed model consists of 1D and 2D filters, and as a result, we can reduce the computational complexity of the existing SR algorithms, with negligible visual loss. The computational complexity of the proposed algorithm is 71.37%, 61.82%, and 50.78% lower in CPU, TPU, and GPU than the very-deep SR (VDSR) algorithm, with a peak signal-to-noise ratio loss of 0.49 dB.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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