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We present the first sublinear-time algorithms for computing order statistics in the Farey sequence and for the related problem of ranking. Our algorithms achieve a running times of nearly O(n 2/3), which is a significant improvement over the previous algorithms taking time O(n). We also initiate the study of a more general problem: counting primitive(More)
Various efficient game problem solvers are based on PN-Search. Especially depth-first versions of PN-Search like DF-PN or PDS – contrary to other known techniques – are able to solve really hard problems. However, the performance of DF-PN and PDS decreases dramatically when the search space significantly exceeds available memory. A simple trick to overcome(More)
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(More)
In recent years the Monte Carlo tree search revolution has spread from computer Go to many areas, including computer Hex. MCTS Hex players now outperform traditional knowledge-based alpha-beta search players, and the reigning Computer Olympiad Hex gold medallist is the MCTS player MoHex. In this paper we show how to strengthen Mo-Hex, and observe that — as(More)
For some two-player games (e.g. Go), no accurate and inexpensive heuristic is known for evaluating leaves of a search tree. For other games (e.g. chess), a heuristic is known (sum of piece values). For other games (e.g. Hex), only a local heuristic — one that compares children reliably, but non-siblings poorly — is known (cell voltage drop in the(More)
The main topic of this contribution is the problem of counting square-free numbers not exceeding n. Before this work we were able to do it in time 1 ˜ O(√ n). Here, the algorithm with time complexity˜O(n 2/5) and with memory complexity˜O(n 1/5) is presented. Additionally, a parallel version is shown, which achieves full scalability. As of now the highest(More)