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 -