A simple on-line bin-packing algorithm
Journal of the ACM (JACM)
Online algorithms for a dual version of bin packing
Discrete Applied Mathematics
Probabilistic analysis of algorithms for dual bin packing problems
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On-line and Off-line Approximation Algorithms for Vector Covering Problems
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Online variable sized covering
Information and Computation
On-Line Variable Sized Covering
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Approximation lower bounds in online LIB bin packing and covering
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the 13th Australasian workshop on combinatorial algorithms
On the on-line rent-or-buy problem in probabilistic environments
Journal of Global Optimization
Bin packing with controllable item sizes
Information and Computation
Theoretical Computer Science
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We deal with the variable-sized bin covering problem: Given a list L of items in (0,1] and a finite collection B of feasible bin sizes, the goal is to select a set of bins with sizes in B and to cover them with the items in L such that the total size of the covered bins is maximized. In the on-line version of this problem, the items must be assigned to bins one by one without previewing future items. This note presents a complete solution to the on-line problem: For every collection B of bin sizes, we give an on-line approximation algorithm with a worst-case ratio r(B), and we prove that no on-line algorithm can perform better in the worst case. The value r(B) mainly depends on the largest gap between consecutive bin sizes.