Indexed by:Conference Paper

Date of Publication:2011-05-28

Included Journals:CPCI-S、EI

Volume:6681

Page Number:176-184

Abstract:In this paper, we study a two-dimensional knapsack problem: packing squares as many as possible into a unit square. Our results are the following:
   (i) first, we propose an algorithm called IHS(Increasing Height Shelf), and prove that the packing is optimal if there are at most 5 squares packed in an optimal packing, and this upper bound 5 is sharp;
   (ii) secondly, if all the items have size(side length) at most 1/k, where k >= 1 is a constant number, we propose a simple algorithm with an approximation ratio k2+3k+2/k2 in time O(n log n).
   (iii) finally, we give a PTAS for the general case, and our algorithm is much simpler than the previous approach[16].