On bin packing with conflicts

Leah Epstein, Asaf Levin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-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 each independent set is at most one, so that the number of independent sets in the partition is minimized. This problem is clearly a generalization of both the classical (one-dimensional) bin packing problem where E = Ø 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 for a sub-class of perfect graphs, which contains interval graphs, and a 7/4 = 1.75-approximation for 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
Title of host publicationApproximation and Online Algorithms - 4th International Workshop, WAOA 2006, Revised Papers
PublisherSpringer Verlag
Number of pages14
ISBN (Print)9783540695134
StatePublished - 2007
Event4th Workshop on Approximation and Online Algorithms, WAOA 2006 - Zurich, Switzerland
Duration: 14 Sep 200615 Sep 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4368 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference4th Workshop on Approximation and Online Algorithms, WAOA 2006

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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