On bin packing with conflicts

Leah Epstein, Asaf Levin

Research output: Contribution to journalArticlepeer-review


We consider the offline and online versions of a bin packing problem called bin packing with conflicts. Given a set of items V= {1,2,..., n} with sizes s1, S2,..., sn ∈ [0,1] and a conflict graph G = (V, E), the goal is to find a partition of the items into independent sets of G, where the total size of items in each independent set is at most 1 so that the number of independent sets in the partition is minimized. This problem is clearly a generalization of both the classical (onedimensional) bin packing problem where E = θ and of the graph coloring problem where Si = 0 for all i = 1,2,..., n. Since coloring problems on general graphs are hard to approximate, following previous work, we study the problem on specific graph classes. For the offline version, we design improved approximation algorithms for perfect graphs and other special classes of graphs: These are a 5/2 = 2.5-approximation algorithm for perfect graphs; a 7/3 ≈ 2.33333-approximation algorithm for a subclass of perfect graphs, which contains interval graphs and chordal graphs; and a 7/4 = 1.75-approximation for algorithm bipartite graphs. For the online problem on interval graphs, we design a 4.7-competitive algorithm and show a lower bound of 155/36 ≈ 4.30556 on the competitive ratio of any algorithm. To derive the last lower bound, we introduce the first lower bound on the asymptotic competitive ratio of any online bin packing algorithm with known optimal value, which is 47/36 ≈ 1.30556.

Original languageEnglish
Pages (from-to)1270-1298
Number of pages29
JournalSIAM Journal on Optimization
Issue number3
StatePublished - 2008


  • Approximation algorithms
  • Bin packing
  • Online algorithms

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science


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