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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Journal Article•
TL;DR: A new two-dimensional pattern complexity is defined via space structure of the figure that can distinguish the two- dimensional figures with different properties and overcomes the defect of MIG complexity.
Abstract: A new two-dimensional pattern complexity is defined via space structure of the figure.This complexity can distinguish the two-dimensional figures with different properties.It overcomes the defect of MIG complexity.
3 citations
TL;DR: A more tight upper bound on the complexity of the LLL algorithm in terms of the condition number and determinant of a given lattice matrix is derived using the proposed upper bound.
Abstract: We analyze the complexity of the LLL algorithm, invented by Lenstra, Lenstra, and Lovasz as a a well-known lattice reduction (LR) algorithm which is previously known as having the complexity of O(N 4 logB) multiplications (or, O(N 5 (logB) 2 ) bit operations) for a lattice basis matrix H(∈ R M×N ) where B is the maximum value among the squared norm of columns of H. This implies that the complexity of the lattice reduction algorithm depends only on the matrix size and the lattice basis norm. However, the matrix structures (i.e., the correlation among the columns) of a given lattice matrix, which is usually measured by its condition number or determinant, can affect the computational complexity of the LR algorithm. In this paper, to see how the matrix structures can affect the LLL algorithm’s complexity, we derive a more tight upper bound on the complexity of LLL algorithm in terms of the condition number and determinant of a given lattice matrix. We also analyze the complexities of the LLL updating/downdating schemes using the proposed upper bound.
3 citations
06 Sep 1994
TL;DR: Two probabilistic models developed in order to predict the computational complexity of the branch and bound algorithm as well as its suitability for a parallelization based on the simultaneous exploration of all subproblems having a same common lower bound are studied.
Abstract: We study two probabilistic models developed in order to predict the computational complexity of the branch and bound algorithm as well as its suitability for a parallelization based on the simultaneous exploration of all subproblems having a same common lower bound We show that both models, starting from different assumptions, yield asymptotically the same results but differ for small problems. Both models agree to predict a quick increase of the number of subproblems as a function of their lower bounds offering a convenient approach for parallelization of the branch and bound algorithm.
3 citations
22 Jun 1992
TL;DR: The difference between NP and other complexity classes is examined and the question of whether an NP-hard set can be approximated sufficiently by the sets in other complexityclasses is studied.
Abstract: The difference between NP and other complexity classes is examined. The question of whether an NP-hard set can be approximated sufficiently by the sets in other complexity classes is studied. >
3 citations
Journal Article•
TL;DR: A novel algorithm for this problem based on dynamic programming is proposed and Simulation results show it is effective and the complexity of the proposed algorithm is analyzed.
Abstract: The dynamic programming algorithm is a flexible and high-efficient method to many problems. In this paper,a kind of change problem is brought up firstly. And then a novel algorithm for this problem based on dynamic programming is proposed. Finally,the complexity of the proposed algorithm is analyzed. Simulation results show it is effective.
3 citations