A min-cut approach to functional regionalization, with a case study of the Italian local labour market areas

In several economical, statistical and geographical applications, a territory must be subdivided into functional regions. Such regions are not fixed and politically delimited, but should be identified by analyzing the interactions among all its constituent localities. This is a very delicate and important task, that often turns out to be computationally difficult. In this work we propose an innovative approach to this problem based on the solution of minimum cut problems over an undirected graph called here transitions graph. The proposed procedure guarantees that the obtained regions satisfy all the statistical conditions required when considering this type of problems. Results on real-world instances show the effectiveness of the proposed approach

Approximation for Maximum Surjective Constraint Satisfaction Problems

Maximum surjective constraint satisfaction problems (Max-Sur-CSPs) are computational problems where we are given a set of variables denoting values from a finite domain B and a set of constraints on the variables. A solution to such a problem is a surjective mapping from the set of variables to B such that the number of satisfied constraints is maximized. We study the approximation performance that can be acccchieved by algorithms for these problems, mainly by investigating their relation with Max-CSPs (which are the corresponding problems without the surjectivity requirement). Our work gives a complexity dichotomy for Max-Sur-CSP(B) between PTAS and APX-complete, under the assumption that there is a complexity dichotomy for Max-CSP(B) between PO and APX-complete, which has already been proved on the Boolean domain and 3-element domains