Vector bin packing with multiple-choice

Boaz Patt-Shamir, Dror Rawitz

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


We consider a variant of bin packing called multiple-choice vector bin packing. In this problem, we are given a set of n items, where each item can be selected in one of several D-dimensional incarnations. We are also given T bin types, each with its own cost andD-dimensional size. Our goal is to pack the items in a set of bins of minimum overall cost. The problem is motivated by scheduling in networks with guaranteed quality of service (QoS), but due to its general formulation it has many other applications as well. We present an approximation algorithm that is guaranteed to produce a solution whose cost is about lnD times the optimum. For the running time to be polynomial we require D=O(1) and T=O(logn). This extends previous results for vector bin packing, in which each item has a single incarnation and there is only one bin type. To obtain our result we also present a PTAS for the multiple-choice version of multidimensional knapsack, where we are given only one bin and the goal is to pack a maximum weight set of (incarnations of) items in that bin.

Original languageEnglish
Pages (from-to)1591-1600
Number of pages10
JournalDiscrete Applied Mathematics
Issue number10-11
StatePublished - Jul 2012
Externally publishedYes

Bibliographical note

Funding Information:
A preliminary version of this work appears in Proc. 12th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT), 2010. Research supported in part by the Next Generation Video (NeGeV) Consortium, Israel.

Funding Information:
The work of Boaz Patt-Shamir was supported in part by the Israel Science Foundation (grant 1372/09 ) and by Israel Ministry of Science and Technology .


  • Approximation algorithms
  • Multiple-choice multidimensional knapsack
  • Multiple-choice vector bin packing


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