Partial Order Constraints for Graph Algorithms

In recent work [5, 6, 1] we formalize a propositional logic over partial orders. Formulæ in this logic are just like usual propositional formulæ except that propositions are statements about a partial order on a finite set of symbols. For example, (f = g)∧ ((f > h) ∨ (h > g)) is a formula in this logic. We refer to the formulæ of this logic as partial order constraints. There are many applications in computer science which involve reasoning about (the satisfiability of) partial order constraints. We have implemented (in Prolog) a solver [4] for partial order constraints. To solve a partial order constraint C we encode it into a corresponding propositional statement φ such that satisfying assignments of φ correspond to solutions of C. The implementation runs on top of a Prolog interface [3] to the MiniSat [7] solver. In this project we will attempt to solve computationally hard graph algorithms by encoding them into Boolean satisfiability and partial order constraint satisfiability problems. We will focus on algorithms which aim to provide some “optimal” order on the vertices of a given graph. Examples are minimal cutwidth [8] and treewidth [2]. Prerequisites: An appreciation of “Introduction to Algorithms”; Willing to download and learn about SAT solvers; Programming in Prolog (an advantage). In the second semester, the course on logic programming will touch upon related topics to this project.