  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.
