1 research outputs found
A Faster FPTAS for the Unbounded Knapsack Problem
The Unbounded Knapsack Problem (UKP) is a well-known variant of the famous
0-1 Knapsack Problem (0-1 KP). In contrast to 0-1 KP, an arbitrary number of
copies of every item can be taken in UKP. Since UKP is NP-hard, fully
polynomial time approximation schemes (FPTAS) are of great interest. Such
algorithms find a solution arbitrarily close to the optimum ,
i.e. of value at least for ,
and have a running time polynomial in the input length and
. For over thirty years, the best FPTAS was due to
Lawler with a running time in and a space
complexity in , where is the number of
knapsack items. We present an improved FPTAS with a running time in and a space bound in
. This directly
improves the running time of the fastest known approximation schemes for Bin
Packing and Strip Packing, which have to approximately solve UKP instances as
subproblems.Comment: 30 pages, pdfLaTeX; typos corrected, additional smaller explanations
to improve readability and to avoid confusion; full version of paper
presented at IWOCA 2015, reviewer comments were taken into accoun