2008/03/29 by Xin Han, Han, Xin, Kazuo Iwama +3
Computer Science · Engineering · #Advanced Manufacturing and Logistics Optimization #Optimization and Packing Problems #Optimization and Search Problems #cs.CC #cs.DS
paper · pdf · doi:10.48550/arxiv.0803.4260
arxiv created 2008/03/29 · arxiv updated 2009/12/01
In this paper, we study the following knapsack problem: Given a list of squares with profits, we are requested to pack a sublist of them into a rectangular bin (not a unit square bin) to make profits in the bin as large as possible. We first observe there is a Polynomial Time Approximation Scheme (PTAS) for the problem of packing weighted squares into rectangular bins with large resources, then apply the PTAS to the problem of packing squares with profits into a rectangular bin and get a \frac65+ε approximation algorithm.