Breaking Instance-Independent Symmetries in Exact Graph Coloring

Abstract

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Naturally-occurring instances of such problems are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 ILP suggests generic problem-reduction methods, rather than problem-specific heuristics, because: (1) heuristics are easily upset by new constraints; (2) heuristics tend to ignore structure; and (3) many relevant problems are provably inapproximable. The NP-spec project offers a language to specify NP-problems and automatic reductions to SAT. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry-breaking, in particular when certain kinds of symmetry are present in all generated instances. Our surprising conclusion is that instance-independent symmetries should often be processed together with instance-specific symmetries rather than earlier, at the specification level.