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- W4386179983 abstract "With the development of sport sliding puzzle, it is of great significance to study better algorithms to solve sliding puzzles. Since solving the puzzle optimally is hard, we hope to find an additive approximation algorithm, that is, the length of solution output by this algorithm is at most a low-order term more than optimal solution. $$ntimes 2$$ rectangular puzzle, as a variation of $$(n^2-1)$$ -puzzle, can be solved by an algorithm in divide-and-conquer scheme. We proved that it’s an additive approximation algorithm within $$O(nlog n)$$ additive constant. For $$(n^2-1)$$ -puzzle, finding a good approximation algorithm is more difficult. We designed a new poly-time algorithm to solve $$(n^2-1)$$ -puzzle, which consists of several phases: First build the board into a “clear state”, then transport the tiles in this clear state, after arranging some tiles the puzzle is divided into smaller parts, finally solve each of parts. And we proved that it is an additive approximation algorithm within $$O(n^{2.75})$$ additive constant. Also, using these approximation algorithms, we analyzed the optimal solution length asymptotically in the average case and the worst case (God’s number). For $$ntimes 2$$ rectangular puzzle, the average optimal solution length is $$n^2+O(nlog n)$$ and the God’s number is $$2n^2+O(nlog n)$$ . For $$(n^2-1)$$ -puzzle, the average optimal solution length is $${2over 3}n^3+O(n^{2.75})$$ and the God’s number is $$n^3+O(n^{2.75})$$ ." @default.
- W4386179983 created "2023-08-26" @default.
- W4386179983 creator A5027666948 @default.
- W4386179983 date "2023-01-01" @default.
- W4386179983 modified "2023-09-28" @default.
- W4386179983 title "Additive Approximation Algorithms for Sliding Puzzle" @default.
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- W4386179983 doi "https://doi.org/10.1007/978-3-031-39344-0_10" @default.
- W4386179983 hasPublicationYear "2023" @default.
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