scholarly journals Combining dynamic programming with filtering to solve a four-stage two-dimensional guillotine-cut bounded knapsack problem

2018 ◽  
Vol 29 ◽  
pp. 18-44 ◽  
Author(s):  
François Clautiaux ◽  
Ruslan Sadykov ◽  
François Vanderbeck ◽  
Quentin Viaud
Keyword(s):  
Dynamic Programming ◽  
Knapsack Problem ◽  
Two Dimensional ◽  
Guillotine Cut

scholarly journals An approximation scheme for the two-stage, two-dimensional knapsack problem

2010 ◽  
Vol 7 (3) ◽  
pp. 114-124 ◽  
Author(s):  
Alberto Caprara ◽  
Andrea Lodi ◽  
Michele Monaci
Keyword(s):  
Knapsack Problem ◽  
Approximation Scheme ◽  
Two Dimensional ◽  
Two Stage

Solving the two-dimensional knapsack problem considering cutting-time and emission of particulate matter in the metalworking industry

2018 ◽  
Vol 16 (12) ◽  
pp. 2888-2895
Author(s):  
Paula A. Velasco Carvajal ◽  
Guillermo Alberto Camacho Munoz ◽  
Daniel Cuellar Usaquen ◽  
David Alvarez-Martinez
Keyword(s):  
Particulate Matter ◽  
Knapsack Problem ◽  
Two Dimensional ◽  
Metalworking Industry

TWO FOR ONE: TIGHT APPROXIMATION OF 2D BIN PACKING

2013 ◽  
Vol 24 (08) ◽  
pp. 1299-1327 ◽  
Author(s):  
ROLF HARREN ◽  
KLAUS JANSEN ◽  
LARS PRÄDEL ◽  
ULRICH M. SCHWARZ ◽  
ROB VAN STEE
Keyword(s):  
Lower Bound ◽  
Knapsack Problem ◽  
Bin Packing ◽  
Packing Problem ◽  
Approximate Algorithm ◽  
Two Dimensional ◽  
Chip Design ◽  
Practical Applications ◽  
Vlsi Chip ◽  
Bin Packing Problem

In this paper, we study the two-dimensional geometrical bin packing problem (2DBP): given a list of rectangles, provide a packing of all these into the smallest possible number of unit bins without rotating the rectangles. Beyond its theoretical appeal, this problem has many practical applications, for example in print layout and VLSI chip design. We present a 2-approximate algorithm, which improves over the previous best known ratio of 3, matches the best results for the problem where rotations are allowed and also matches the known lower bound of approximability. Our approach makes strong use of a PTAS for a related 2D knapsack problem and a new algorithm that can pack instances into two bins if OPT = 1.

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