An Improved Approximation Scheme for Variable-Sized Bin Packing

A faster FPTAS for the Unbounded Knapsack Problem

“…The AFPTAS by Shachnai and Yehezkely [25] has the same additive term and a running time in O( 1 ε 6 log 3 ( 1 ε ) + log( 1 ε )n) for general instances. Currently, the AFPTAS in [10] has the smallest additive term f ( The first AFPTAS for Strip Packing was presented by Kenyon and Rémila [19] with f (…”

“…Both algorithms in [2,10] solve UKP instances for column generation. A faster FPTAS for UKP therefore directly yields faster AFPTAS for Bin Packing and Strip Packing.…”

“…The goal is to find the best knapsack size and corresponding solution of maximum profit. UKPIP is used for column generation in our AFPTAS for Variable-Sized Bin Packing [10] where several bin sizes are given and the goal is to minimize the total volume of the bins used. The faster FPTAS for UKPIP yields a faster AFPTAS for Variable-Sized Bin Packing [20].…”

“…Let KP (d, ε) be the running time to find a (1 − ε) approximate solution to a UKP instance with d items. The Bin Packing algorithm in [10] has the running time…”