Introduction to the Special Issue on Global Constraints

Global constraints go back to the early 1990s, where they were introduced into CHIP in order to deal with problems from the industrial partners of the European Research Computer Centre. Since then, they have become widespread and are today present in all industrial solvers (i.e., ECLAIR by Thales, ECLiPSe by Cisco, Ilog Solver by Ilog, Koalog Solver by Koalog) as well as in most academic solvers (i.e., CHOCO, FaCile, Gecode, JaCoP, Mozart, SICStus). The third article of this special issue, “Models for Global Constraint Applications,” provides an overview of some industrial applications from key areas such as assignment, scheduling and timetabling, where Constraint Programming has been quite successful. In the early 1990s, constraint technology was largely based on general-purpose methods from Artificial Intelligence. These methods turned out not to be sufficiently effective, which led to some disappointment with constraint technology. This in turn led to the introduction of global constraints relying on effective and efficient algorithms. The filtering algorithms behind many common global constraints are in fact based on well-known theorems from discrete mathematics. For instance, the alldifferent and the colored-matrix constraints of J.-C. Regin are respectively based on a corollary of C. Berge, which characterises the arcs of a graph that belong to a maximum matching but not to all, and a generalisation of the “Matrix composed of 0s and 1s” problem by L.R. Ford and D.R. Fulkerson. The first article of this special issue, “Arc-B-Consistency for the Inter-Distance Constraint,” belongs to this line of