Scalable Parallel DFPN Search

We present Scalable Parallel Depth-First Proof Number Search, a new shared-memory parallel version of depth-first proof number search. Based on the serial DFPN 1+ε method of Pawlewicz and Lew, SPDFPN searches effectively even as the transposition table becomes almost full, and so can solve large problems. To assign jobs to threads, SPDFPN uses proof and disproof numbers and two parameters. SPDFPN uses no domain-specific knowledge or heuristics, so it can be used in any domain. Our experiments show that SPDFPN scales well and performs well on hard problems. We tested SPDFPN on problems from the game of Hex. On a 24-core machine and a 4.2-hour single-thread task, parallel efficiency ranges from 0.8 on 4 threads to 0.74 on 16 threads. SPDFPN solved all previously intractable 9×9 Hex opening moves; the hardest opening took 111 days. Also, in 63 days, it solved one 10×10 Hex opening move. This is the first time a computer or human has solved a 10×10 Hex opening move.