Worst-Case Complexity Bounds on Algorithms for Computing the Canonical Structure of Infinite Abelian Groups and Solving Systems of Linear Diophantine Equations

1989 ◽  
Vol 18 (4) ◽  
pp. 670-678 ◽  
Author(s):  
Costas S. Iliopoulos
Keyword(s):  
Diophantine Equations ◽  
Abelian Groups ◽  
Canonical Structure ◽  
Worst Case ◽  
Complexity Bounds ◽  
Case Complexity ◽  
Linear Diophantine Equations ◽  
Worst Case Complexity

scholarly journals Soft clustering by convex electoral model

2020 ◽  
Vol 24 (23) ◽  
pp. 17609-17620 ◽  
Author(s):  
Yurii Nesterov
Keyword(s):  
Time Complexity ◽  
Unique Fixed Point ◽  
Multidimensional Data ◽  
Worst Case ◽  
Complexity Bounds ◽  
Soft Clustering ◽  
Case Complexity ◽  
Worst Case Complexity ◽  
Direct Minimization ◽  
A New Technique

AbstractIn this paper, we suggest a new technique for soft clustering of multidimensional data. It is based on a new convex voting model, where each voter chooses a party with certain probability depending on the divergence between his/her preferences and the position of the party. The parties can react on the results of polls by changing their positions. We prove that under some natural assumptions this system has a unique fixed point, providing a unique solution for soft clustering. The solution of our model can be found either by imitation of the sequential elections, or by direct minimization of a convex potential function. In both cases, the methods converge linearly to the solution. We provide our methods with worst-case complexity bounds. To the best of our knowledge, these are the first polynomial-time complexity results in this field.

scholarly journals On the optimal order of worst case complexity of direct search

2015 ◽  
Vol 10 (4) ◽  
pp. 699-708 ◽  
Author(s):  
M. Dodangeh ◽  
L. N. Vicente ◽  
Z. Zhang
Keyword(s):  
Direct Search ◽  
Optimal Order ◽  
Worst Case ◽  
Case Complexity ◽  
Worst Case Complexity

Worst-case Complexity of Exact Algorithms forNP-hard Problems

2010 ◽  
pp. 203-240
Author(s):  
Federico Della Croce ◽  
Bruno Escoffier ◽  
Marcin Kamiski ◽  
Vangelis Th. Paschos
Keyword(s):  
Exact Algorithms ◽  
Worst Case ◽  
Case Complexity ◽  
Worst Case Complexity ◽  
Hard Problems
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