TY - GEN

T1 - Multi-dimensional packing with conflicts

AU - Epstein, Leah

AU - Levin, Asaf

AU - Van Stee, Rob

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=38149072982&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-74240-1_25

DO - 10.1007/978-3-540-74240-1_25

M3 - Conference contribution

AN - SCOPUS:38149072982

SN - 9783540742395

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

SP - 288

EP - 299

BT - Fundamentals of Computation Theory - 16th International Symposium, FCT 2007, Proceedings

PB - Springer Verlag

T2 - 16th International Symposium on Fundamentals of Computation Theory, FCT 2007

Y2 - 27 August 2007 through 30 August 2007

ER -