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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)

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)

We present the rst 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 signicant improvement over the previous algorithms taking time O(n). We also initiate the study of a more general problem: counting primitive lattice… (More)

The paper presents the first sublinear algorithm for computing order statistics in the Farey sequences. The algorithm runs in time O(n 3/4 log n) and in space O(√ n) for Farey sequence of order n. This is a significant improvement to the algorithm from [1] that runs in time O(n log n).

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)

Recently we introduced Sibling Conspiracy Number Search — an algorithm based not on evaluation of leaf states of the search tree but, for each node, on relative evaluation scores of all children of that node — and implemented an SCNS Hex bot. Here we show the strength of SCNS features: most critical is to initialize leaves via a multi-step process. Also, we… (More)

—For connection games such as Hex or Y or Havan-nah, finding guaranteed cell-to-cell connection strategies can be a computational bottleneck. In automated players and solvers, sets of such virtual connections are often found with Anshelevich's H-search algorithm: initialize trivial connections, and then repeatedly apply an AND-rule (for combining… (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)