Strip Packing with Slicing

In the strip packing problem, a given set of axis-aligned rectangles must be packed into a fixed-width strip, and the goal is to minimize the height of the strip. In this paper, we examine a variant in which each rectangle may be cut vertically into multiple slices and the slices may be packed into the strip as individual pieces. Our results are: (1) analysis of the approximation ratio of several simple heuristics based on first fit and shelf techniques; (2) a simple polynomial algorithm with approximation factor 5/3 for the case where each rectangle can only be sliced once; (3) a fully polynomial time approximation scheme (FPTAS).