Topic
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.
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23 May 2010
TL;DR: In this paper, the computational complexity of optimum decoding for an orthogonal space-time block code is quantified and four equivalent techniques for optimum decoding which have the same computational complexity are specified.
Abstract: The computational complexity of optimum decoding for an orthogonal space-time block code is quantified. Four equivalent techniques of optimum decoding which have the same computational complexity are specified. Modifications to the basic formulation in special cases are calculated and illustrated by means of examples.
5 citations
TL;DR: This special issue aims to present a small sample of papers that are representative of the different types of results that have been obtained in average-case complexity, e.g., whether NP = P implies that NP has problems that are hard on average.
Abstract: Average-case complexity, which examines the tractability of computational problems on ‘random instances,’ is a major topic in complexity theory with at least two distinct motivations. On one hand, it may provide a more realistic model than worst-case complexity for the problem instances actually encountered in practice. On the other hand, it provides us with methods to generate hard instances, allowing us to harness intractability for useful ends such as cryptography and derandomization. These two motivations are actually supported by a variety of different notions of average-case complexity (surveyed in [17, 13, 6]) and relating these notions is an important direction for research in the area. An even more ambitious goal is to understand the relationship between average-case complexity and worst-case complexity, e.g., whether NP = P implies that NP has problems that are hard on average. In recent years, there has been substantial progress on this front. This special issue aims to present a small sample of papers that are representative of the different types of results that have been obtained:
5 citations
07 May 1996
TL;DR: An approach to adaptive IIR filtering based on a pseudo-linear regression and a QR matrix decomposition is developed that has proved to be stable and has good convergence properties if the unknown system satisfies the strictly positive real condition.
Abstract: An approach to adaptive IIR filtering based on a pseudo-linear regression and a QR matrix decomposition is developed. The algorithm has proved to be stable and has good convergence properties if the unknown system satisfies the strictly positive real condition. The derivation of the algorithm is straightforward and the computational complexity is less than the computational complexity of the IIR-RPE algorithm. Simulation results of system identification with synthetic and real world data are shown comparing the algorithm with the IIR-RPE and the IIR-LMS algorithm.
5 citations
26 Jun 2012
TL;DR: It is a remarkable fact that two prominent problems of algebraic complexity theory, the permanent versus determinant problem and the tensor rank problem (matrix multiplication), can be restated as explicit orbit closure problems, and asymptotic versions of the the latter questions are of relevance in quantum information theory.
Abstract: It is a remarkable fact that two prominent problems of algebraic complexity theory, the permanent versus determinant problem and the tensor rank problem (matrix multiplication), can be restated as explicit orbit closure problems. This offers the potential to prove lower complexity bounds by relying on methods from algebraic geometry and representation theory. While this basic idea for the tensor rank problem goes back to work by Volker Strassen from the mid eighties, the geometric complexity program has gained visibility and momentum in the past years. Some modest lower bounds for border rank have recently been proven by the construction of explicit obstructions. For further progress, a better understanding of irreducible representions of symmetric groups (tensor products and plethysms) is required. Interestingly, asymptotic versions of the the latter questions are of relevance in quantum information theory.
5 citations
01 Jan 2000
TL;DR: A new sequence pair algorithm is introduced which has complexity lower than O(M’.25), which is a significant improvement compared to the original O( M2) algorithm.
Abstract: This paper introduces a new sequence pair algorithm which has complexity lower than O(M’.25), which is a significant improvement compared to the original O(M2) algorithm [l]. Furthermore, the new algorithm has complexity close to the theoretical lower bound. Experimental results, obtained with a straightforward implementation, confirm this improvement in complexity.
5 citations