Journal Article10.1137/0209062
Performance Bounds for Level-Oriented Two-Dimensional Packing Algorithms
549
TL;DR: 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.
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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.
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Citations
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.
914
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.
Approximation Algorithms for Bin-Packing — An Updated Survey
Edward G. Coffman,Michael Randolph Garey,David S. Johnson +2 more
- 01 Jan 1984
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].
490
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.
401
Heuristic and Metaheuristic Approaches for a Class of Two-Dimensional Bin Packing Problems
TL;DR: A new heuristic algorithm for each problem in the class of problems arising from all combinations of the above requirements, and a unified tabu search approach that is adapted to a specific problem by simply changing the heuristic used to explore the neighborhood.
382
References
•Book
Computer and job-shop scheduling theory
Edward G. Coffman,John L. Bruno +1 more
- 01 Jan 1976
1.2K
Worst-Case Performance Bounds for Simple One-Dimensional Packing Algorithms
TL;DR: This work examines the performance of a number of simple algorithms which obtain “good” placements and shows that neither the first-fit nor the best-fit algorithm will ever use more than $\frac{17}{10}L^ * + 2$ bins.
1K
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.
Performance Guarantees for Scheduling Algorithms
TL;DR: This paper presents an introduction to this approach to scheduling by describing its application to a well-known multiprocessor scheduling model and illustrating the variety of algorithms and results that are possible.
155