Indexed by:期刊论文

Date of Publication:2013-10-14

Journal:THEORETICAL COMPUTER SCIENCE

Included Journals:SCIE、EI、Scopus

Volume:508

Page Number:35-40

ISSN No.:0304-3975

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) we propose an algorithm called IHS (Increasing Height Shelf), and prove that the packing is optimal if in an optimal packing there are at most 5 squares, and this upper bound is sharp;
   (ii) if all the squares have side length at most 1/k., we propose a simple and fast algorithm with an approximation ratio k(2)-3k+2/k(2) in time O(n log n);
   (iii) we give an EPTAS for the problem, where the previous result in Jansen and Solis-Oba (2008)[16] is a PTAS, not an EPTAS. However our approach does not work on the previous model of Jansen and Solis-Oba (2008) [16], where each square has an arbitrary weight. (C) 2012 Elsevier B.V. All rights reserved.