A simple on-line bin-packing algorithm
Journal of the ACM (JACM)
On-line bin packing in linear time
Journal of Algorithms
On the worst-case performance of the NKF bin-packing heuristic
Acta Cybernetica
Tight worst-case performance bounds for next-k-fit bin packing
SIAM Journal on Computing
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
New Algorithms for Bin Packing
Journal of the ACM (JACM)
On the sum-of-squares algorithm for bin packing
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Introduction to Algorithms
On the online bin packing problem
Journal of the ACM (JACM)
A Self Organizing Bin Packing Heuristic
ALENEX '99 Selected papers from the International Workshop on Algorithm Engineering and Experimentation
An efficient fully polynomial approximation scheme for the Subset-Sum problem
Journal of Computer and System Sciences
A sublinear-time approximation scheme for bin packing
Theoretical Computer Science
Fast algorithms for bin packing
Journal of Computer and System Sciences
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Given a set S = {b1, ..., bn} of integers and an integer s, the subset sum problem is to decide if there is a subset S′ of S such that the sum of elements in S′ is exactly equal to s. We present an online approximation scheme for this problem. It updates in O(log n) time and gives a (1+ε)-approximation solution in O((log n+ 1/ε2 (log 1/ε)O(1)) log n) time. The online approximation for target s is to find a subset of the items that have been received. The bin packing problem is to find the minimum number of bins of size one to pack a list of items a1, ..., an of size in [0, 1]. Let function bp(L) be the minimum number of bins to pack all items in the list L. We present an online approximate algorithm for the function bp(L) in the bin packing problem, where L is the list of the items that have been received. It updates in O(log n) updating time and gives a (1 + ε)-approximation solution app(L) for bp(L) in O((log n)2 + (1/ε)O(1/ε)) time to satisfy app(L) ≤ (1 + ε)bp(L) + 1.