An APTAS for Bin Packing with Clique-graph Conflicts [article]

Ilan Doron-Arad, Ariel Kulik, Hadas Shachnai
2021 arXiv   pre-print
We study the following variant of the classic bin packing problem. Given a set of items of various sizes, partitioned into groups, find a packing of the items in a minimum number of identical (unit-size) bins, such that no two items of the same group are assigned to the same bin. This problem, known as bin packing with clique-graph conflicts, has natural applications in storing file replicas, security in cloud computing and signal distribution. Our main result is an asymptotic polynomial time
more » ... proximation scheme (APTAS) for the problem, improving upon the best known ratio of 2. particular, for any instance I and a fixed ∈ (0,1), the items are packed in at most (1+)OPT(I) +1 bins, where OPT(I) is the minimum number of bins required for packing the instance. As a key tool, we apply a novel Shift & Swap technique which generalizes the classic linear shifting technique to scenarios allowing conflicts between items. The major challenge of packing small items using only a small number of extra bins is tackled through an intricate combination of enumeration and a greedy-based approach that utilizes the rounded solution of a linear program.
arXiv:2011.04273v6 fatcat:2ay62rfv45fz5gjukgxw6y5fnm