Waldo Gálvez, F. Grandoni, Sandy Heydrich, Salvatore Ingala, A. Khan, Andreas Wiese
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引用次数: 35
摘要
我们研究了二维几何背包问题(2DK)，在这个问题中，我们得到了一组n个轴对齐的矩形物品，每个物品都有一个相关的利润，以及一个轴对齐的方形背包。目标是找到背包内物品(不旋转物品)的最大利润子集的(非重叠)包装。这个问题最著名的多项式时间近似因子(即使只是在基数情况下)是2+ε[Jansen and Zhang, SODA, 2004]。在本文中，我们打破了2近似障碍，实现了多项式时间17/9 + ε
We study the two-dimensional geometric knapsack problem (2DK) in which we are given a set of n axis-aligned rectangular items, each one with an associated profit, and an axis-aligned square knapsack. The goal is to find a (non-overlapping) packing of a maximum profit subset of items inside the knapsack (without rotating items). The best-known polynomial-time approximation factor for this problem (even just in the cardinality case) is 2+ε [Jansen and Zhang, SODA 2004]. In this paper we break the 2 approximation barrier, achieving a polynomialtime 17/9 + ε
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