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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04 Aug 2001TL;DR: It is shown suprisingly that AC-3 achieves the optimal worst case time complexity with O(ed2), the result is applied to obtain a path consistency algorithm which has the same time and space complexity as the best known theoretical results.
Abstract: The AC-3 algorithm is a basic and widely used arc consistency enforcing algorithm in Constraint Satisfaction Problems (CSP). Its strength lies in that it is simple, empirically efficient and extensible. However its worst case time complexity was not considered optimal since the first complexity result for AC-3 [Mackworth and Freuder, 1985] with the bound O(ed3), where e is the number of constraints and d the size of the largest domain. In this paper, we show suprisingly that AC-3 achieves the optimal worst case time complexity with O(ed2). The result is applied to obtain a path consistency algorithm which has the same time and space complexity as the best known theoretical results. Our experimental results show that the new approach to AC-3 is comparable to the traditional AC-3 implementation for simpler problems where AC-3 is more efficient than other algorithms and significantly faster on hard instances.
106 citations
TL;DR: In this article, the authors survey the average-case complexity of problems in NP and present completeness results due to Impagliazzo and Levin, and discuss various notions of good-on-average algorithms.
Abstract: We survey the average-case complexity of problems in NP.
We discuss various notions of good-on-average algorithms, and present completeness results due to Impagliazzo and Levin. Such completeness results establish the fact that if a certain specific (but somewhat artificial) NP problem is easy-on-average with respect to the uniform distribution, then all problems in NP are easy-on-average with respect to all samplable distributions. Applying the theory to natural distributional problems remain an outstanding open question. We review some natural distributional problems whose average-case complexity is of particular interest and that do not yet fit into this theory.
A major open question is whether the existence of hard-on-average problems in NP can be based on the P ≠ NP assumption or on related worst-case assumptions. We review negative results showing that certain proof techniques cannot prove such a result. While the relation between worst-case and average-case complexity for general NP problems remains open, there has been progress in understanding the relation between different "degrees" of average-case complexity. We discuss some of these "hardness amplification" results.
105 citations
TL;DR: In this article, the authors gave the first construction of pseudorandom generators from a uniform complexity assumption on EXP (namely EXP ≠ BPP), but their result does not provide a continuous trade-off between worst-case hardness and pseudo-randomness.
Abstract: Impagliazzo and Wigderson (1998) gave the first construction of pseudorandom generators from a uniform complexity assumption on EXP (namely EXP ≠ BPP). Unlike results in the nonuniform setting, their result does not provide a continuous trade-off between worst-case hardness and pseudorandomness, nor does it explicitly establish an average-case hardness result.
In this paper:
102 citations
20 Mar 2006
TL;DR: In this paper, an exact algorithm for motif extraction based on suffix trees is presented, which is shown to be more than two times faster than the best known exact algorithm in terms of average case complexity.
Abstract: We present in this paper an exact algorithm for motif extraction. Efficiency is achieved by means of an improvement in the algorithm and data structures that applies to the whole class of motif inference algorithms based on suffix trees. An average case complexity analysis shows a gain over the best known exact algorithm for motif extraction. A full implementation was developed and made available online. Experimental results show that the proposed algorithm is more than two times faster than the best known exact algorithm for motif extraction.
102 citations
14 Nov 2014
TL;DR: An attempt is made to develop an O(n) complexity (linear order) counterpart of the k-means, which includes a directional movement of intermediate clusters and thereby improves compactness and separability properties of cluster structures simultaneously.
Abstract: The k-means algorithm is known to have a time complexity of O (n 2), where n is the input data size. This quadratic complexity debars the algorithm from being effectively used in large applications. In this article, an attempt is made to develop an O (n) complexity (linear order) counterpart of the k-means. The underlying modification includes a directional movement of intermediate clusters and thereby improves compactness and separability properties of cluster structures simultaneously. This process also results in an improved visualization of clustered data. Comparison of results obtained with the classical k-means and the present algorithm indicates usefulness of the new approach.
101 citations