Average-case complexity

About: Average-case complexity is a research topic. Over the lifetime, 1749 publications have been published within this topic receiving 44972 citations.

A novel algorithm for number factorization

Abstract: This paper presents a novel algorithm for number factorization, which makes use of some classical calculus theory for real functions. An iterative procedure is constructed that searches for specific features of the image values in a function related with the factorization of the number. Studies of the complexity of the method are being performed and its applicability to very large numbers is being tested. In general, the method can be implemented in a very simple manner and shows promising applicability in RSA encryption.

The Time Complexity Analysis for a Kind of Neural Network with Rational Spline Functions

Abstract: Based on the results of weight function neural networks, the time complexity for a kind of neural network with rational spline functions is analyzed. We derive the complexity results by interpolation theories and algorithms. We find a linear relationship between the time complexity and the number of patterns. We also conclude that the time complexity is proportional to the input and output dimensions of the neural network. It shows that the results proposed in this paper have many potential applications. KEYWORD: Neural Network; Rational Spline Function; Weight Function; Time Complexity

On the equivalence of a reduced-complexity recursive power normalization algorithm and the exponential window power estimation

Abstract: The transform-domain least-mean-square (TD-LMS) algorithm provides significantly faster convergence than the LMS algorithm for coloured input signals. However, a major disadvantage of the TD-LMS algorithm is the large computational complexity arising from the unitary transform and power normalization operations. In this paper we establish the equivalence of a recently proposed recursive power normalization algorithm and the traditional exponential window power estimation algorithm. The proposed algorithm is based on the matrix inversion lemma and is optimized for implementation on a digital signal processor (DSP). It reduces the number of divisions from N to one for a TD-LMS adaptive filter with N coefficients. This provides a significant reduction in computational complexity for DSP implementations. The equivalence of the reduced-complexity algorithm and the exponential window power estimation algorithm is demonstrated in simulation examples.

A near-ML sphere constraint stack detection algorithm with very low complexity in VBLAST systems

Abstract: The stack algorithm is a promising tree-search algorithm with relatively low computation complexity for multi-input multi-output (MIMO) systems. Recent researches show that it obtains low detection complexity at the price of performance degradation. To achieve a better compromise between computational complexity and detection performance, a sphere constraint stack detection algorithm (SC-Stack) is proposed in this paper. With the aid of sorted QR decomposition based on the MMSE criterion (MMSE-SQRD), the proposed algorithm constrains conventional stack algorithm by a sphere radius obtained from partial serial interference cancellation (PSIC) algorithm. The SC-Stack algorithm avoids abundant metric computation by excluding a large number of nodes from the stack according to the sphere radius. The simulation results of computational complexity and detection performance presented in this paper show that the SC-Stack algorithm improves detection performance with lower complexity than the conventional stack algorithm. Moreover, the proposed algorithm achieves almost the same performance as sphere decoding algorithm while expanding far fewer nodes. So it is more feasible in practical systems.