Solving Set Constraint Satisfaction Problems using ROBDDs

Constraint solvers typically maintain a domain of possible values for each variable that may form part of a solution to a constraint satisfaction problem. Historically, it has been thought impractical to represent precisely the domains of certain types of constrained variable, such as finite set variables. For example, the domain of a finite set variable which can take on the value of any subset of {1, . . . , N} contains 2N elements, which when using a näıve representation quickly becomes unmanageable even for small N . Instead, most finite set solvers have resorted to maintaining an approximation to the true domain of a set variable, typically described by upper and lower bounds under the subset partial ordering relation. However, Lagoon and Stuckey have demonstrated a new approach to modelling finite domain constraint problems using Reduced Ordered Binary Decision Diagrams (ROBDDs), which is particularly applicable to set variables and set domains. Building on their work, which showed that it is possible to construct an efficient set domain propagator which compactly represents many set domains and set constraints using ROBDDs, we demonstrate that the ROBDD-based approach provides unprecedented flexibility in modelling constraint satisfaction problems, leading to performance improvements. We show that the ROBDD-based modelling approach can be extended to the modelling of integer and multiset constraint problems in a straightforward manner. Since domain propagation is not always practical, we also show how to incorporate less strict consistency notions into the ROBDD framework, such as set bounds, cardinality bounds and lexicographic bounds consistency. Finally, we present experimental results that demonstrate the ROBDD-based solver performs better than various more conventional constraint solvers on several standard set constraint problems. Supervisor: Peter J. Stuckey I would like to express my gratitude both to Peter Stuckey and to Vitaly Lagoon, whose guidance and assistance made this thesis possible. Thanks also to my parents and friends for keeping me more sane than I otherwise would be.