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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08 Sep 2014TL;DR: The used criteria are adequate for predicting the mean execution time and its confidence intervals for given input types in an algorithm complexity as a random value research.
Abstract: A statistical research of an algorithm complexity as a random value was carried out via numerical experimentation using parallel computation. For a segment of input data sizes point characteristics for this random value and its confidence interval are obtained. Confidence complexity function value based on gamma-distribution is determined. The following result have been obtained: the used criteria are adequate for predicting the mean execution time and its confidence intervals for given input types.
6 citations
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TL;DR: An article on codiagnosability verification of discrete event systems was reported by Moreira et al, claiming an improvement in complexity over a paper by Qiu and Kumar, but the results were obtained in a more restricted setting of “projection mask”, in contrast to the more general “non-projection masks” allowed in Qiu & Kumar's paper.
Abstract: An article on codiagnosability verification of discrete event systems was reported by Moreira et al, claiming an improvement in complexity over a paper by Qiu and Kumar. This note clarifies an oversight in the complexity analysis of Moreira et al's paper. Further the results of Moreira et al's paper were obtained in a more restricted setting of “projection masks”, in contrast to the more general “non-projection masks” allowed in Qiu and Kumar's paper, which was overlooked. Finally in the special case when the projection masks are used, the complexity of Qiu and Kumar's paper is lower compared to the non-projection masks case, and equals the corrected complexity of Moreira et al's paper.
6 citations
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16 Jul 2001TL;DR: It is concluded that there exist regular languages the roots of which are not even context-sensitive, and that the quadratic time complexity for deciding the set of all primitive words by an 1-tape Turing machine is optimal.
Abstract: The root of a language L is the set of all primitive words p such that pn belongs to L for some n ? 1. We show that the gap between the time complexity and space complexity, respectively, of a language and that of its root can be arbitrarily great. From this we conclude that there exist regular languages the roots of which are not even context-sensitive. Also we show that the quadratic time complexity for deciding the set of all primitive words by an 1-tape Turing machine is optimal.
6 citations
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TL;DR: This work presents a hierarchy theorem for average-case complexity, for arbitrary time-bounds, that is as tight as the well-known Hartmanis-Stearns HS65], and demonstrates that the deenition is natural and is as justiied for arbitrary Time-Bounds as is Levin's deenitions for polynomial time- bounds.
Abstract: We extend Levin's theory of average polynomial time to arbitrary time-bounds in accordance with the following general principles: (1) It essentially agrees with Levin's notion when applied to polynomial time-bounds. (2) If a language L belongs to DTIME(T(n)), for some time-bound T (n), then every distributional problem (L;) is T on the-average. (3) If L does not belong to DTIME(T(n)) almost everywhere, then no distributional problem (L;) is T on the-average. We present a hierarchy theorem for average-case complexity, for arbitrary time-bounds, that is as tight as the well-known Hartmanis-Stearns HS65] hierarchy theorem for deterministic complexity. As a consequence, for every time-bound T (n), there are distributional problems (L;) that can be solved using only a slight increase in time but that cannot be solved on the-average in time T (n). We demonstrate that our deenition is natural and is as justiied for arbitrary time-bounds as is Levin's deenition for polynomial time-bounds. We critique an earlier proposal of a deenition of average case complexity for arbitrary time-bounds BDCGL92] by demonstrating that it does not satisfy our general principles. Nevertheless, we obtain a ne hierarchy, for the earlier deenition, for distributional problems whose running time is bounded by a polynomial. Our proofs use techniques of convexity, HH older's inequality, and properties of Hardy's class of logarithmico-exponential functions.
6 citations
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14 May 2012TL;DR: A suboptimal user grouping algorithm is provided which substantially reduces complexity compared to the optimum Hungarian algorithm with negligible capacity degradation and outperforms the greedy algorithm with a considerable lower complexity.
Abstract: In this paper, we investigate user grouping for cooperative scheduling in a two-cell network. When the number of transmitters grows large, the complexity of the Hungarian algorithm optimum for user pairing becomes unaffordable in real-time systems. We consider user grouping algorithms maximizing the network sum rate in cells with a massive number of terminals and/or sensors. We provide a suboptimal user grouping algorithm which substantially reduces complexity compared to the optimum Hungarian algorithm with negligible capacity degradation. Surprisingly, the proposed algorithm outperforms the greedy algorithm with a considerable lower complexity.
6 citations