著者

Amanj Khorramian Tomoko Taniguchi Takeaki Uno Ryuhei Uehara

雑誌

研究報告アルゴリズム(AL) (ISSN:21888566)

巻号頁・発行日

vol.2018-AL-168, no.2, pp.1-8, 2018-05-18

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Othello, also known as Reversi, is a quite well known strategy board game for two players on a board of size 8 ×8. The set of all reachable patterns is not yet known for this game. In this paper, we finally obtain all reachable patterns on 5 × 6 board by developing nontrivial algorithm on a supercomputer. We observe the scale of complete search-tree is big even for a board of size 5 × 6 and parallelize a distributed frontier search using shared memory to reach the final depth of the tree. To reduce the memory requirement, the tree is horizontally compressed using a novel method, and the frontiers are maintained in a novel data-structure. Moreover, an efficient number system is proposed and utilized for representing the states of the game, and a symmetry of the states is applied during the search. We assume that the board and pattern are rotation symmetry, but we assume that the mirror symmetry gives the different pattern. Eventually, the whole tree is traversed in 2 hours by visiting 257,387,474,170 different states using random access memory shared among 576 processing cores. We aim to find specific font patterns among the states of the final depth. However, 83,175,694 of the states are located at the final depth, at which we start looking for font patterns. Before that, a set of 96 characters of size 6 × 6 is binarized, and their (5 × 6)-compatible patterns are taken for lookup by considering all possible symmetries. In this way, a font of 96 characters is designed.