Lower Bounds on the Performance of Online Algorithms for Relaxed Packing Problems

We prove new lower bounds for suitable competitive ratio measures of two relaxed online packing problems: removable multiple knapsack, and a recently introduced minimum peak appointment scheduling problem. The high level objective in both problems is to pack arriving items sizes at most 1 into bins capacity as efficiently possible, but the exact formalizations differ. In problem, every item has be assigned position, which can seen time interval during workday length 1. That is, are not bins, only once all processed, optimal number subject chosen positions determined, this cost algorithm. On other hand, knapsack problem there fixed goal items, consists choosing particular bin packed (and nothing else), valuable subset possible. last it possible reject that deliberately them, well remove any later point time, adds flexibility