TY - GEN

T1 - On bin packing with conflicts

AU - Epstein, Leah

AU - Levin, Asaf

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=38149015499&partnerID=8YFLogxK

U2 - 10.1007/11970125_13

DO - 10.1007/11970125_13

M3 - Conference contribution

AN - SCOPUS:38149015499

SN - 9783540695134

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 160

EP - 173

BT - Approximation and Online Algorithms - 4th International Workshop, WAOA 2006, Revised Papers

PB - Springer Verlag

T2 - 4th Workshop on Approximation and Online Algorithms, WAOA 2006

Y2 - 14 September 2006 through 15 September 2006

ER -