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Several Methods of Analysis for Cardinality Constrained Bin Packing

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Approximation and Online Algorithms (WAOA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12982))

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Abstract

We consider a known variant of bin packing called cardinality constrained bin packing, also called bin packing with cardinality constraints (BPCC). In this problem, there is a parameter \(k\ge 2\), and items of rational sizes in [0, 1] are to be packed into bins, such that no bin has more than k items or total size larger than 1. The goal is to minimize the number of bins.

A recently introduced concept, called the price of clustering, deals with inputs that are presented in a way that they are split into clusters. Thus, an item has two attributes which are its size and its cluster. The goal is to measure the relation between an optimal solution that cannot combine items of different clusters into bins, and an optimal solution that can combine items of different clusters arbitrarily. Usually the number of clusters may be large, while clusters are relatively small, though not trivially small. Such problems are related to greedy bin packing algorithms, and to batched bin packing, which is similar to the price of clustering, but there is a constant number of large clusters. We analyze the price of clustering for BPCC, including the parametric case with bounded item sizes. We discuss several greedy algorithms for this problem that were not studied in the past, and comment on batched bin packing.

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Authors and Affiliations

  1. Department of Mathematics, University of Haifa, Haifa, Israel

    Leah Epstein

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  1. Leah Epstein
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Correspondence to Leah Epstein .

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Editors and Affiliations

  1. University of Waterloo, Waterloo, ON, Canada

    Jochen Koenemann

  2. RWTH Aachen University, Aachen, Germany

    Britta Peis

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Epstein, L. (2021). Several Methods of Analysis for Cardinality Constrained Bin Packing. In: Koenemann, J., Peis, B. (eds) Approximation and Online Algorithms. WAOA 2021. Lecture Notes in Computer Science(), vol 12982. Springer, Cham. https://doi.org/10.1007/978-3-030-92702-8_8

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  • DOI: https://doi.org/10.1007/978-3-030-92702-8_8

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