On the sum minimization version of the online bin covering problem

Authors:
János Csirik;Leah Epstein;Csanád Imreh;Asaf Levin
Affiliations:
Department of Informatics, University of Szeged, Árpád tér 2, H-6720 Szeged, Hungary;Department of Mathematics, University of Haifa, 31905 Haifa, Israel;Department of Informatics, University of Szeged, Árpád tér 2, H-6720 Szeged, Hungary;Chaya fellow. Faculty of Industrial Engineering and Management, The Technion, 32000 Haifa, Israel
Venue:
Discrete Applied Mathematics
Year:
2010

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Abstract

Given a set of m identical bins of size 1, the online input consists of a (potentially infinite) stream of items in (0,1]. Each item is to be assigned to a bin upon arrival. The goal is to cover all bins, that is, to reach a situation where a total size of items of at least 1 is assigned to each bin. The cost of an algorithm is the sum of all used items at the moment when the goal is first fulfilled. We consider three variants of the problem, the online problem, where there is no restriction of the input items, and the two semi-online models, where the items arrive sorted by size, that is, either by non-decreasing size or by non-increasing size. The offline problem is considered as well.