A Polynomial Approximation Scheme for Scheduling on Uniform Processors: Using the Dual Approximation Approach

1988 ◽  
Vol 17 (3) ◽  
pp. 539-551 ◽  
Author(s):  
Dorit S. Hochbaum ◽  
David B. Shmoys
Keyword(s):  
Polynomial Approximation ◽  
Approximation Scheme ◽  
Approximation Approach ◽  
Uniform Processors

Maximizing the Number of Visible Labels on a Rotating Map

2021 ◽  
Vol 31 (2) ◽  
pp. 293-313
Author(s):  
Ali Gholami Rudi ◽  
Keyword(s):  
Polynomial Approximation ◽  
Approximation Scheme ◽  
Geometric Object ◽  
Np Hard ◽  
Feature Points ◽  
New Variant ◽  
Vertical Bars ◽  
The Individual

For a map that can be rotated, we consider the following problem. There are a number of feature points on the map, each having a geometric object as a label. The goal is to find the largest subset of these labels such that when the map is rotated and the labels remain vertical, no two labels in the subset intersect. We show that, even if the labels are vertical bars of zero width, this problem remains NP-hard, and present a polynomial approximation scheme for solving it. We also introduce a new variant of the problem for vertical labels of zero width, in which any label that does not appear in the output must be coalesced with a label that does. Coalescing a subset of the labels means to choose a representative among them and set its label height to the sum of the individual label heights.

scholarly journals An efficient fully polynomial approximation scheme for the Subset-Sum Problem

2003 ◽  
Vol 66 (2) ◽  
pp. 349-370 ◽  
Author(s):  
Hans Kellerer ◽  
Renata Mansini ◽  
Ulrich Pferschy ◽  
Maria Grazia Speranza
Keyword(s):  
Polynomial Approximation ◽  
Approximation Scheme ◽  
Subset Sum Problem ◽  
Fully Polynomial Approximation Scheme ◽  
Subset Sum
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