Journal ArticleDOI
Performance Bounds for Level-Oriented Two-Dimensional Packing Algorithms
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TLDR
This work analyzes several “level-oriented” algorithms for packing rectangles into a unit-width, infinite-height bin and gives more refined bounds for special cases in which the widths of the given rectangles are restricted and in which only squares are to be packed.Abstract:
We analyze several “level-oriented” algorithms for packing rectangles into a unit-width, infinite-height bin so as to minimize the total height of the packing. For the three algorithms we discuss, we show that the ratio of the height obtained by the algorithm to the optimal height is asymptotically bounded, respectively, by 2, 1.7, and 1.5. The latter two improve substantially over the performance bounds for previously proposed algorithms. In addition, we give more refined bounds for special cases in which the widths of the given rectangles are restricted and in which only squares are to be packed.read more
Citations
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Journal ArticleDOI
Two-dimensional packing problems: A survey
TL;DR: This work considers problems requiring to allocate a set of rectangular items to larger rectangular standardized units by minimizing the waste by discussing mathematical models, lower bounds, classical approximation algorithms, recent heuristic and metaheuristic methods and exact enumerative approaches.
Journal ArticleDOI
Orthogonal Packings in Two Dimensions
TL;DR: Efficient approximation algorithms are devised, their limitations are studied, and worst-case bounds on the performance of the packings they produce are derived.
Journal ArticleDOI
An Exact Two-Dimensional Non-Guillotine Cutting Tree Search Procedure
TL;DR: A Lagrangean relaxation of a zero-one integer programming formulation of the problem of cutting a number of rectangular pieces from a single large rectangle is developed and used as a bound in a tree search procedure.
Book ChapterDOI
Approximation Algorithms for Bin-Packing — An Updated Survey
TL;DR: This paper updates a survey written about 3 years ago with many new results, some of which represent important advances, and more than doubles the list in [53].
Journal ArticleDOI
Exact Solution of the Two-Dimensional Finite Bon Packing Problem
Silvano Martello,Daniele Vigo +1 more
TL;DR: This work analyzes a well-known lower bound of the Two-Dimensional Finite Bin Packing Problem, and proposes not lower bounds which are used within a branch-and-bound algorithm for the exact solution of the problem.
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