Modes of transition from imperfection sensitivity to imperfection insensitivity

From imperfection to nonidealness

Beyond perfection, the field to be explored is too wide. In this context, several ways to classify imperfect graphs or, equivalently, 0, 1 (clique-node) imperfect matrices can be found in the literature. From the polyhedral point of view, ideal matrices are to set covering problems what perfect matrices are to set packing problems. In fact, if a matrix is ideal, its linear relaxation is an inte...

Imperfection-sensitivity and Catastrophe Theory

Understanding Imperfection

Because of their inherent abstraction, systems ideas are not themselves sufficient for gaining scientific knowledge or solving practical problems, but they can be a source of insights into the universality of imperfection, insights which can contribute to a new scientific world view. Systems theory offers a metaphysics, or more precisely an ontology, of imperfection. Through it, we can heed Spi...

Graph Imperfection

We are interested in colouring a graph G=(V, E) together with an integral weight or demand vector x=(xv : v # V) in such a way that xv colours are assigned to each node v, adjacent nodes are coloured with disjoint sets of colours, and we use as few colours as possible. Such problems arise in the design of cellular communication systems, when radio channels must be assigned to transmitters to sa...

Comparing Imperfection Ratio and Imperfection Index for Graph Classes

Perfect graphs constitute a well-studied graph class with a rich structure, reflected by many characterizations with respect to different concepts. Perfect graphs are, for instance, precisely those graphs G where the stable set polytope STAB(G) coincides with the fractional stable set polytope QSTAB(G). For all imperfect graphs G it holds that STAB(G) ⊂ QSTAB(G). It is, therefore, natural to us...