Minimum weighted sum bin packing

Authors:
Leah Epstein;Asaf Levin
Affiliations:
Department of Mathematics, University of Haifa, Haifa, Israel;Department of Statistics, The Hebrew University, Jerusalem, Israel
Venue:
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Year:
2007

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Abstract

We study MINIMUM WEIGHTED SUM BIN PACKING (MWSBP), which is a bin packing problem where the cost of an item is the index of the bin into which it is packed multiplied by its weight, and the goal is to minimize the total cost of the items. This is equivalent to a batch scheduling problem which we define, where the total weighted completion time is to be minimized. This problem is previously known to be NP-hard in the strong sense even for unit weight items. We design a polynomial time approximation scheme for it, and additionally, a dual polynomial time approximation scheme.