Online bin covering with limited migration

Abstract

Semi-online models where decisions may be revoked in a limited way have been studied extensively in the last years. A well-studied measure of the amount of decisions that can be revoked is the (constant) migration factor. When an object arrives, the decisions for objects of total size at most the migration factor times its size may be revoked. This means that a small object only leads to small changes. We extensively study the bin covering problem with migration in different scenarios. We develop algorithms both for the static case where only insertions are allowed, and for the dynamic case, where items may also depart. We also develop lower bounds for these scenarios both for amortized migration and for worst-case migration showing that our algorithms have nearly optimal migration factor and asymptotic competitive ratio. We therefore resolve the competitiveness of the bin covering problem with migration.