Fekete and Schepers' graph-based algorithm for the two-dimensional orthogonal packing problem revisited

Abstract

In this paper Fekete and Schepers' exact algorithm for the non-guillotinable two-dimensional orthogonal packing problem is discussed. A modification to this algorithm is also proposed. The Fekete and Schepers' algorithm relies on a graph representation of packing patterns to assess if there is a feasible packing for a problem. Yet, the algorithm's projection graphs construction mechanism sometimes degenerates and while it correctly assesses the existence of a feasible packing pattern, the resulting projection graphs are not equal to the graphs of the packing class to which the packing pattern belongs [1] [2]. The presented algorithm overcomes this problem by introducing an extra condition to avoid the aforementioned degeneration. This modification was tested over instances of previously published literature.