Improved Constant-Time Approximation Algorithms for Maximum Matchings and Other Optimization Problems

2012 ◽  
Vol 41 (4) ◽  
pp. 1074-1093 ◽  
Author(s):  
Yuichi Yoshida ◽  
Masaki Yamamoto ◽  
Hiro Ito
Keyword(s):  
Approximation Algorithms ◽  
Optimization Problems ◽  
Constant Time ◽  
Time Approximation

APPROXIMATING THE DIAMETER, WIDTH, SMALLEST ENCLOSING CYLINDER, AND MINIMUM-WIDTH ANNULUS

2002 ◽  
Vol 12 (01n02) ◽  
pp. 67-85 ◽  
Author(s):  
TIMOTHY M. CHAN
Keyword(s):  
Approximation Algorithms ◽  
Approximation Algorithm ◽  
Optimization Problems ◽  
Linear Time ◽  
Minimum Width ◽  
Time Approximation ◽  
Running Time ◽  
Fixed Dimension ◽  
Smallest Enclosing Cylinder ◽  
Point Set

We study (1+ε)-factor approximation algorithms for several well-known optimization problems on a given n-point set: (a) diameter, (b) width, (c) smallest enclosing cylinder, and (d) minimum-width annulus. Among our results are new simple algorithms for (a) and (c) with an improved dependence of the running time on ε, as well as the first linear-time approximation algorithm for (d) in any fixed dimension. All four problems can be solved within a time bound of the form O(n+ε-c) or O(n log (1/ε)+ε-c).

scholarly journals Pointwise observation of the state given by complex time lag parabolic system

2017 ◽  
Vol 27 (1) ◽  
pp. 77-89
Author(s):  
Adam Kowalewski
Keyword(s):  
Boundary Condition ◽  
Parabolic System ◽  
Neumann Boundary Condition ◽  
Optimization Problems ◽  
Time Lag ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
The State ◽  
Constant Time ◽  
Time Lags

AbstractVarious optimization problems for linear parabolic systems with multiple constant time lags are considered. In this paper, we consider an optimal distributed control problem for a linear complex parabolic system in which different multiple constant time lags appear both in the state equation and in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic time lag equation with the Neumann boundary condition are proved. The time horizon T is fixed. Making use of the Lions scheme [13], necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functional with pointwise observation of the state and constrained control are derived. The example of application is also provided.

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