In combinatorial reconfiguration, the reconfiguration problems on a vertex subset (e.g., an independent set) are well investigated. In these problems, some tokens are placed on a subset of vertices of the graph, and there are three natural reconfiguration rules called ``token sliding,'' ``token jumping,'' and ``token addition and removal''. In the context of computational complexity of puzzles, the sliding block puzzles play an important role. Depending on the rules and set of pieces, the sliding block puzzles characterize the computational complexity classes including P, NP, and PSPACE. The sliding block puzzles correspond to the token sliding model in the context of combinatorial reconfiguration. On the other hand, a relatively new notion of jumping block puzzles is proposed in puzzle society. This is the counterpart to the token jumping model of the combinatorial reconfiguration problems in the context of block puzzles. We investigate several variants of jumping block puzzles and determine their computational complexities.

中文翻译：

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跳跃块拼图的计算复杂度

在组合重构中，顶点子集（例如，独立集）上的重构问题得到了很好的研究。在这些问题中，一些标记被放置在图的一个顶点子集上，存在三种自然重构规则，称为“标记滑动”、“标记跳跃”和“标记添加和移除”。在拼图计算复杂度的背景下，滑块拼图发挥着重要作用。根据规则和碎片集，滑块拼图表征计算复杂度类别，包括 P、NP 和 PSPACE。滑块拼图对应于组合重构上下文中的令牌滑动模型。另一方面，拼图社会提出了一种相对较新的跳跃拼图概念。这是块拼图上下文中组合重配置问题的令牌跳跃模型的对应物。我们研究了跳跃拼图的几种变体并确定了它们的计算复杂性。