Approximating Geometric Knapsack via L-Packings

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