Solving Set Constraint Satisfaction Problems using ROBDDs

In this paper we present a new approach to modeling finite set domain constraint problems using Reduced Ordered Binary Decision Diagrams (ROBDDs). We show 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 modeling constraint satisfaction problems, leading to performance improvements. We also show that the ROBDD-based modeling approach can be extended to the modeling 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

On Path Consistency for Binary Constraint Satisfaction Problems

Constraint satisfaction problems (CSPs) provide a flexible and powerful framework for modeling and solving many decision problems of practical importance. Consistency properties and the algorithms for enforcing them on a problem instance are at the heart of Constraint Processing and best distinguish this area from other areas concerned with the same combinatorial problems. In this thesis, we study path consistency (PC) and investigate several algorithms for enforcing it on binary finite CSPs. We also study algorithms for enforcing consistency properties that are related to PC but are stronger or weaker than PC. We identify and correct errors in the literature and settle an open question. We propose two improvements that we apply to the well-known algorithms PC-8 and PC-2001, yielding PC-8+ and PC-2001+. Further, we propose a new algorithm for enforcing partial path consistency, σ-∆-PPC, which generalizes features of the well-known algorithms DPC and PPC. We evaluate over fifteen different algorithms on both benchmark and randomly generated binary problems to empirically demonstrate the effectiveness of our approach. Adviser: Berthe Y. Choueir

On Source Coding with Coded Side Information for a Binary Source with Binary Side Information

The lossless rate region for the coded side information problem is "solved," but its solution is expressed in terms of an auxiliary random variable. As a result, finding the rate region for any fixed example requires an optimization over a family of allowed auxiliary random variables. While intuitive constructions are easy to come by and optimal solutions are known under some special conditions, proving the optimal solution is surprisingly difficult even for examples as basic as a binary source with binary side information. We derive the optimal auxiliary random variables and corresponding achievable rate regions for a family of problems where both the source and side information are binary. Our solution involves first tightening known bounds on the alphabet size of the auxiliary random variable and then optimizing the auxiliary random variable subject to this constraint. The technique used to tighten the bound on the alphabet size applies to a variety of problems beyond the one studied here