Divide and Conquer and Dynamic Programming

2021 ◽  
pp. 247-288
Author(s):  
Thomas Mailund
Keyword(s):  
Dynamic Programming ◽  
Divide And Conquer

scholarly journals Deriving divide-and-conquer dynamic programming algorithms using solver-aided transformations

2016 ◽  
Vol 51 (10) ◽  
pp. 145-164 ◽  
Author(s):  
Shachar Itzhaky ◽  
Rohit Singh ◽  
Armando Solar-Lezama ◽  
Kuat Yessenov ◽  
Yongquan Lu ◽  
...  
Keyword(s):  
Dynamic Programming ◽  
Divide And Conquer ◽  
Programming Algorithms

FIXED PARAMETER ALGORITHMS FOR THE MINIMUM WEIGHT TRIANGULATION PROBLEM

2008 ◽  
Vol 18 (03) ◽  
pp. 185-220 ◽  
Author(s):  
MAGDALENE GRANTSON BORGELT ◽  
CHRISTIAN BORGELT ◽  
CHRISTOS LEVCOPOULOS
Keyword(s):  
Dynamic Programming ◽  
Time Complexity ◽  
Minimum Weight ◽  
Simple Polygon ◽  
Divide And Conquer ◽  
The Core ◽  
Fixed Parameter ◽  
Minimum Weight Triangulation ◽  
Divide And Conquer Scheme

We discuss and compare four fixed parameter algorithms for finding the minimum weight triangulation of a simple polygon with (n – k) vertices on the perimeter and k vertices in the interior (hole vertices), that is, for a total of n vertices. All four algorithms rely on the same abstract divide-and-conquer scheme, which is made efficient by a variant of dynamic programming. They are essentially based on two simple observations about triangulations, which give rise to triangle splits and paths splits. While each of the first two algorithms uses only one of these split types, the last two algorithms combine them in order to achieve certain improvements and thus to reduce the time complexity. By discussing this sequence of four algorithms we try to bring out the core ideas as clearly as possible and thus strive to achieve a deeper understanding as well as a simpler specification of these approaches. In addition, we implemented all four algorithms in Java and report results of experiments we carried out with this implementation.

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