Improved Approximation for Two Dimensional Strip Packing with Polynomial Bounded Width

We study the well-known two-dimensional strip packing problem. Given is a set of rectangular axis-parallel items and a strip of width W with infinite height. The objective is to find a packing of these items into the strip, which minimizes the packing height. Lately, it has been shown that the lower bound of 3/2 of the absolute approximation ratio can be beaten when we allow a pseudo-polynomial running-time of type (nW ). If W is polynomially bounded by the number of items, this is a polynomial running-time. We present a pseudopolynomial algorithm with approximation ratio 4/3 + ε and running time (nW ) O(21/ε ) .