Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
Analysis of Several Task-Scheduling Algorithms for a Model of Multiprogramming Computer Systems
Journal of the ACM (JACM)
Algorithms for on-line bin-packing problems with cardinality constraints
Discrete Applied Mathematics
Parallelism versus Memory Allocation in Pipelined Router Forwarding Engines
Theory of Computing Systems
Online Bin Packing with Cardinality Constraints
SIAM Journal on Discrete Mathematics
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Approximation schemes for packing with item fragmentation
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Improved results for a memory allocation problem
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Note: Approximation of the k-batch consolidation problem
Theoretical Computer Science
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We continue the study of bin packing with splittable items and cardinality constraints. In this problem, a set of items must be packed into as few bins as possible. Items may be split, but each bin may contain at most k (parts of) items, where k is some fixed constant. Complicating the problem further is the fact that items may be larger than 1, which is the size of a bin. We close this problem by providing a polynomial-time approximation scheme for it. We first present a scheme for the case k = 2 and then for the general case of constant k. Additionally, we present dual approximation schemes for k = 2 and constant k. Thus we show that for any Ɛ 0, it is possible to pack the items into the optimal number of bins in polynomial time, if the algorithm may use bins of size 1 + Ɛ.