On Bin Packing with Conflicts

Abstract. 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 = 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 perf...

• Type: Journal
• Year: 2008
• Where: SIAMJO
• Authors: Leah Epstein, Asaf Levin
• Keywords: Bin Packing Problem, Independent Sets, Online Versions, SIAMJO 2008