Fekete and Schepers’ graph-based algorithm for the two-dimensional orthogonal packing problem revisited Eduarda Pinto Ferreira 1 , José Fernando Oliveira 2,3 1 ISEP – Instituto Superior de Engenharia do Porto, Portugal eduadapf@gmail.com 2 FEUP – Faculdade de Engenharia da Universidade do Porto, Portugal jfo@fe.up.pt 3 INESC Porto – Instituto de Engenharia de Sistemas e Computadores do Porto, Portugal 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. Keywords: interval graphs, packing. 1 Introduction The problem of cutting a rectangle into smaller rectangular pieces of given sizes is known as the two-dimensional packing problem. It arises in many industries where materials are cut, but it also occurs in less obvious contexts such as machine scheduling or optimisation of the layout of advertisements in newspapers. According to Wäscher’s et al typology [3] this is a SKP problem, as the small items with fixed orientation are processed one by one, without taking into account eventual replications. In this paper we will deal with the associated decision problem of knowing if a given set of rectangles fit into the finite size container: the 2D-OPP. We start by presenting the concept of visibility graph and how it can be used to characterize a packing. For a set of graphs to represent a feasible packing (all the rectangles fit in the container and do not overlap each other), some conditions must be met, as described in section 2. Graph-based algorithms for generating a packing are presented in section 3, starting with a brief description of the original Fekete and Schepers’ algorithm [1]. The presented algorithm is based on the Fekete and Schepers’ algorithm but introduces a supplementary condition that leads to packings for which the minimal interval representations are exactly the ones of the graphs of