In a first time we draw a rough shape of a general formal framework for polynomial approximation theory which encompasses the existing one by allowing the expression of new types of results. We show how this framework incorporates all the existing approximation results and, moreover, how new...

We analyze the approximation behaviour of some of the best-known polynomial time approximation algorithms for bin-packing under an approximation criterion, called differential ratio. This measure has originally been introduced by Ausiello, D'Atri and Protasi and more recently revisited, in a...

We first study the competitivity ratio for the on-line version of the problem of finding a maximum-order induced subgraph satisfying some hereditary property, under the hypothesis that the input graph is revealed by clusters. Next, we focus ourselves on two of the most known instantiations of...

We devise an approximation-preserving reduction of expansion O between weighted and unweighted versions of a class of problems called weighted hereditary induced-subgraph maximisation problems. This allows us to perform a first improvement of the best approximation ratio for the weighted...

We draw a rough shape of a general formal framework for polynomial approximation theory which encompasses the existing one by allowing the expression of new types of results. We show how this framework incorporates all the existing approximation results and, moreover, how new types of results...