Scalable parallel numerical constraint solver using global load balancing

We present a scalable parallel solver for numerical constraint satisfaction problems (NCSPs). Our parallelization scheme consists of homogeneous worker solvers, each of which runs on an available core and communicates with others via the global load balancing (GLB) method. The search tree of the branch and prune algorithm is split and distributed through the two phases of GLB: a random workload stealing phase and a workload distribution and termination phase based on a hyper-cube-shaped graph called lifeline. The parallel solver is simply implemented with X10 that provides an implementation of GLB as a library. In experiments, NCSPs from the literature were solved and attained up to 516-fold speedup using 600 cores of the TSUBAME2.5 supercomputer. Optimal GLB configurations are analyzed.