Dynamic Symmetry Breaking Restarted

Recently, structural symmetry breaking (SSB), a new technique for breaking all piecewise variable and value symmetry in constraint satisfaction problems (CSPs), was introduced. As of today, it is unclear whether the heavy symmetry filtering that SSB performs is at all worthwhile. This paper has two aims: First, we assess the feasibility of SSB. To this end, we introduce the first random benchmark generator that produces CSP instances with piecewise symmetric variables and values of constrainedness. It allows us to evaluate SSB on different regions of constrainedness. Secondly, we study how symmetry breaking and restarts interact. We propose practical enhancements of SSB that allow us to re-use symmetry no-goods in subsequent restarts efficiently. With those enhancements, we find that symmetry breaking can actually benefit from restarts. However, the improvements to be gained by restarting are far smaller than those that can be obtained for methods that break only some symmetries or none at all. Surprisingly, we find that a combination of restarts and breaking value symmetry only can be competitive with, or even be superior to, complete symmetry breaking.