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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.


Papers
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Proceedings ArticleDOI
03 Jan 1991
TL;DR: New lower bounds are presented that give (1) randomization is more powerful than determinism in $k-round protocols, and (2) an explicit function which exhibits an exponential gap between its $k$ and $(k-1)$-round randomized complexity.
Abstract: The $k$-round two-party communication complexity was studied in the deterministic model by [14] and [4] and in the probabilistic model by [20] and [6]. We present new lower bounds that give (1) randomization is more powerful than determinism in $k$-round protocols, and (2) an explicit function which exhibits an exponential gap between its $k$ and $(k-1)$-round randomized complexity. We also study the three party communication model, and exhibit an exponential gap in 3-round protocols that differ in the starting player. Finally, we show new connections of these questions to circuit complexity, that motivate further work in this direction.

116 citations

Book
27 Aug 2008
TL;DR: This paper discusses decision problems in Public Key Cryptography, the Asymptotically Dominant Properties of Cryptanalysis, and length-Based and Quotient Attacks.
Abstract: Background on Groups, Complexity, and Cryptography.- Background on Public Key Cryptography.- Background on Combinatorial Group Theory.- Background on Computational Complexity.- Non-commutative Cryptography.- Canonical Non-commutative Cryptography.- Platform Groups.- Using Decision Problems in Public Key Cryptography.- Generic Complexity and Cryptanalysis.- Distributional Problems and the Average-Case Complexity.- Generic Case Complexity.- Generic Complexity of NP-complete Problems.- Asymptotically Dominant Properties and Cryptanalysis.- Asymptotically Dominant Properties.- Length-Based and Quotient Attacks.

116 citations

Journal ArticleDOI
TL;DR: An O(log n) time wait-free approximate agreement algorithm is presented; the complexity of this algorithm is within a small constant of the lower bound.
Abstract: The time complexity of wait-free algorithms in “normal” executions, where no failures occur and processes operate at approximately the same speed, is considered. A lower bound of log n on the time complexity of any wait-free algorithm that achieves approximate agreement among n processes is proved. In contrast, there exists a non-wait-free algorithm that solves this problem in constant time. This implies an O(log n) time separation between the wait-free and non-wait-free computation models. On the positive side, we present an O(log n) time wait-free approximate agreement algorithm; the complexity of this algorithm is within a small constant of the lower bound.

114 citations

Journal ArticleDOI
TL;DR: The Smyth-completeness of the complexity space and the compactness of closed complexity spaces which possess a (complexity) lower bound have been investigated in this paper, where the complexity analysis of Divide and Conquer algorithms has been studied.

113 citations

Book
01 Jun 1974

112 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20222
20216
202010
20199
201810
201732