Separating codes and traffic monitoring

Abstract

This paper studies the problem of traffic monitoring which consists in differentiating a set of walks on a directed graphs by placing sensors on as few arcs as possible. The problem of characterising a set of individuals by testing as few attributes as possible is already wellknown but traffic monitoring presents new challenges that the previous models of separation fall short at modelling such as taking into account the multiplicity and order of the arcs in a walk. We therefore introduce a new stronger model of separation based on languages that generalises the traffic monitoring problem. We study two subproblems that we think are especially relevant for practical applications and develop methods to solve them combining integer linear programming, separating codes and language theory.