Lower bounds and reduction procedures for the bin packing problem
Discrete Applied Mathematics - Combinatorial Optimization
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Computers and Operations Research
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A new algorithm for optimal bin packing
Eighteenth national conference on Artificial intelligence
Heuristic and Exact Algorithms for the Identical Parallel Machine Scheduling Problem
INFORMS Journal on Computing
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
An improved algorithm for optimal bin packing
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
A hybrid recursive multi-way number partitioning algorithm
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
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The bin-packing problem is to partition a multiset of n numbers into as few bins of capacity C as possible, such that the sum of the numbers in each bin does not exceed C. We compare two existing algorithms for solving this problem: bin completion (BC) and branch-and-cut-and-price (BCP). We show experimentally that the problem difficulty and dominant algorithm are a function of n, the precision of the input elements and the number of bins in an optimal solution. We describe three improvements to BC which result in a speedup of up to five orders of magnitude as compared to the original BC algorithm. While the current belief is that BCP is the dominant bin-packing algorithm, we show that improved BC is up to five orders of magnitude faster than a state-of-the-art BCP algorithm on problems with relatively few bins. We then explore a closely related problem, the number-partitioning problem, and show that an algorithm based on improved bin packing is up to three orders of magnitude faster than a BCP solver called DIMM which claims to be state of the art. Finally, we show how to use number partitioning to generate difficult bin-packing instances.