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Multi-dimensional Packing with Conflicts

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Fundamentals of Computation Theory (FCT 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4639))

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Abstract

We study the multi-dimensional version of the bin packing problem with conflicts. We are given a set of squares V = { 1,2, ...,n} with sides s 1,s 2, ...,s n  ∈ [0,1] and a conflict graph G = (V,E). We seek to find a partition of the items into independent sets of G, where each independent set can be packed into a unit square bin, such that no two squares packed together in one bin overlap. The goal is to minimize the number of independent sets in the partition.

This problem generalizes the square packing problem (in which we have E = ∅) and the graph coloring problem (in which s i  = 0 for all i = 1,2, ...,n). It is well known that coloring problems on general graphs are hard to approximate. Following previous work on the one-dimensional problem, we study the problem on specific graph classes, namely, bipartite graphs and perfect graphs.

We design a 2 + ε-approximation for bipartite graphs, which is almost best possible (unless P = NP). For perfect graphs, we design a 3.2744-approximation.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Haifa, 31905 Haifa, Israel

    Leah Epstein

  2. Department of Statistics, The Hebrew University, Jerusalem 91905, Israel

    Asaf Levin

  3. Department of Computer Science, University of Karlsruhe, D-76128 Karlsruhe, Germany

    Rob van Stee

Authors
  1. Leah Epstein
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  2. Asaf Levin
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  3. Rob van Stee
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Editor information

Erzsébet Csuhaj-Varjú Zoltán Ésik

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© 2007 Springer-Verlag Berlin Heidelberg

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Epstein, L., Levin, A., van Stee, R. (2007). Multi-dimensional Packing with Conflicts. In: Csuhaj-Varjú, E., Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 2007. Lecture Notes in Computer Science, vol 4639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74240-1_25

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  • DOI: https://doi.org/10.1007/978-3-540-74240-1_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74239-5

  • Online ISBN: 978-3-540-74240-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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