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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.


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Proceedings ArticleDOI
01 Jan 2016
TL;DR: In this paper, the authors studied the computational complexity of constraint satisfaction problems that are based on integer expressions and algebraic circuits and showed that the complexity varies over a wide range of complexity classes such as L, P, NP, PSPACE, NEXP, and even Sigma_1, the class of c.e.
Abstract: We study the computational complexity of constraint satisfaction problems that are based on integer expressions and algebraic circuits. On input of a finite set of variables and a finite set of constraints the question is whether the variables can be mapped onto finite subsets of N (resp., finite intervals over N) such that all constraints are satisfied. According to the operations allowed in the constraints, the complexity varies over a wide range of complexity classes such as L, P, NP, PSPACE, NEXP, and even Sigma_1, the class of c.e. languages.

6 citations

Book ChapterDOI
06 Apr 2011
TL;DR: Two approximation methods featuring linear time complexity are proposed for finding a digital hyperplane that contains the largest possible number of points in a bounded grid in dimension d.
Abstract: We consider the following fitting problem: given an arbitrary set of N points in a bounded grid in dimension d, find a digital hyperplane that contains the largest possible number of points. We first observe that the problem is 3SUM-hard in the plane, so that it probably cannot be solved exactly with computational complexity better than O(N2), and it is conjectured that optimal computational complexity in dimension d is in fact O(Nd). We therefore propose two approximation methods featuring linear time complexity. As the latter one is easily implemented, we present experimental results that show the runtime in practice.

6 citations

Proceedings Article
01 Jan 2013
TL;DR: The computational complexity of Shakashaka is determined by proving that Shakashka is NP-complete, and furthermore that counting the number of solutions if #P-complete.
Abstract: Shakashaka is a pencil-and-paper puzzle proposed by Guten and popularized by the Japanese publisher Nikoli (like Sudoku). We determine the computational complexity by proving that Shakashaka is NP-complete, and furthermore that counting the number of solutions if #P-complete. Next we formulate Shakashaka as an integer programming (IP) problem, and show that an IP solver can solve every instance from Nikoli’s website within a second.

6 citations

Journal ArticleDOI
TL;DR: A related algorithm is presented that obtains the linear complexity of the sequence requiring, on average for sequences of period 2n,n≥0, no more than 2 parity checks sums.
Abstract: The linear complexity of a periodic binary sequence is the length of the shortest linear feedback shift register that can be used to generate that sequence. When the sequence has least period 2 n ,n≥0, there is a fast algorithm due to Games and Chan that evaluates this linear complexity. In this paper a related algorithm is presented that obtains the linear complexity of the sequence requiring, on average for sequences of period 2 n ,n≥0, no more than 2 parity checks sums.

6 citations

Book ChapterDOI
01 Jan 2004
TL;DR: It is shown that for the case that N = pfl p is an odd prime,and q is a primitive root modulo p2, the relationship between thelinear complexity and the minimum value of k for which the k-error linear complexity is strictly less than the linear complexity.
Abstract: The k-error linear complexity of an N-periodic sequence with terms in the finite field \({\mathbb{F}_q}\) is defined to be the smallest linear complexity that can be obtained by changing k or fewer terms of the sequence per period. For the case that N = pfl p is an odd prime,and q is a primitive root modulo p2, we show a relationship between the linear complexity and the minimum value of k for which the k-error linear complexity is strictly less than the linear complexity.

6 citations


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