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 shape a formal framework for distinguishing the behaviour of constructive and non-constructive polynomial time approximation algorithms for NP optimization problems. We introduce a new class, called SubNPO, that includes NPO and also some other problems used in recent works.

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...

In this paper, we define and study a new class of optimal stochastic control problems which is closely related to the theory of Backward SDE's and forward-backward SDE's. The controlled process takes values in RXR and a given initial data for X(O). Then, the control problem is to find the...

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...