Multi-dimensional packing with conflicts

Leah Epstein, Asaf Levin, Rob Van Stee

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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, s2, . . . , sn ∈ [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 = φ) and the graph coloring problem (in which si = 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.

Original languageEnglish
Title of host publicationFundamentals of Computation Theory - 16th International Symposium, FCT 2007, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783540742395
StatePublished - 2007
Event16th International Symposium on Fundamentals of Computation Theory, FCT 2007 - Budapest, Hungary
Duration: 27 Aug 200730 Aug 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4639 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference16th International Symposium on Fundamentals of Computation Theory, FCT 2007

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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