Generalizing Global Constraints Based on Network Flows

Global constraints are used in constraint programming to help users specify patterns that occur frequently in the real world. In addition, global constraints facilitate the use of efficient constraint propagation algorithms for problem solving. Many of the most common global constraints used in constraint programming use filtering algorithms based on network flow theory. We show how we can formulate global constraints such as GCC, Among, and their combinations, in terms of a tractable set-intersection problem called Two Families Of Sets (TFOS). We demonstrate that the TFOS problem allows us to represent tasks that are often difficult to model in terms of a classical constraint satisfaction paradigm. In the final part of the paper we specify some tractable and intractable extensions of the TFOS problem. The contribution of this paper is the characterisation of a general framework that helps us to study the tractability of global constraints that rely on filtering algorithms based on network flow theory.