An Exact Algorithm for the Two-Dimensional Stage-Unrestricted Guillotine Cutting/Packing Decision Problem

2016 ◽  
Vol 28 (4) ◽  
pp. 703-720 ◽  
Author(s):  
Krzysztof Fleszar
Keyword(s):  
Decision Problem ◽  
Exact Algorithm ◽  
Two Dimensional ◽  
Guillotine Cutting

scholarly journals A note on compact and compact circular edge-colorings of graphs

2008 ◽  
Vol Vol. 10 no. 3 (Graph and Algorithms) ◽  
Author(s):  
Dariusz Dereniowski ◽  
Adam Nadolski
Keyword(s):  
Approximation Algorithm ◽  
Decision Problem ◽  
Edge Coloring ◽  
Exact Algorithm ◽  
Weighted Graphs ◽  
Edge Colorings ◽  
Odd Cycle ◽  
International Audience ◽  
Np Complete ◽  
Odd Cycles

Graphs and Algorithms International audience We study two variants of edge-coloring of edge-weighted graphs, namely compact edge-coloring and circular compact edge-coloring. First, we discuss relations between these two coloring models. We prove that every outerplanar bipartite graph admits a compact edge-coloring and that the decision problem of the existence of compact circular edge-coloring is NP-complete in general. Then we provide a polynomial time 1:5-approximation algorithm and pseudo-polynomial exact algorithm for compact circular coloring of odd cycles and prove that it is NP-hard to optimally color these graphs. Finally, we prove that if a path P2 is joined by an edge to an odd cycle then the problem of the existence of a compact circular coloring becomes NP-complete.

On a Genetic-Tabu Search Based Algorithm for Two-Dimensional Guillotine Cutting Problems

2012 ◽  
Vol 4 (2) ◽  
pp. 26-40 ◽  
Author(s):  
Hamza Gharsellaoui ◽  
Hamadi Hasni
Keyword(s):  
Tabu Search ◽  
Hybrid Approach ◽  
Search Method ◽  
Two Dimensional ◽  
Whole Number ◽  
Infinite Height ◽  
Tabu Search Method ◽  
Problem Instances ◽  
Cutting Problems ◽  
Guillotine Cutting

The paper deals with the purpose of one hybrid approach for solving the constrained two-dimensional cutting (2DC) problem. The authors study this hybrid approach that combines the genetic algorithm and the Tabu search method. For this problem, they assume a packing of a whole number of rectangular pieces to cut, and that all cuts are of guillotine type in one sheet of a fixed width and an infinite height. Finally, they undertake an extensive experimental study with a large number of problem instances extracted from the literature by the Hopper’s benchmarks in order to support and to prove their approach and to evaluate the performance.

Sign in / Sign up

Export Citation Format

Share Document