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- W2949880204 abstract "Suppose that we are given two independent sets $I_0$ and $I_r$ of a graph such that $|I_0| = |I_r|$, and imagine that a token is placed on each vertex in $I_0$. The token jumping problem is to determine whether there exists a sequence of independent sets which transforms $I_0$ into $I_r$ so that each independent set in the sequence results from the previous one by moving exactly one token to another vertex. This problem is known to be PSPACE-complete even for planar graphs of maximum degree three, and W[1]-hard for general graphs when parameterized by the number of tokens. In this paper, we present a fixed-parameter algorithm for the token jumping problem on planar graphs, where the parameter is only the number of tokens. Furthermore, the algorithm can be modified so that it finds a shortest sequence for a yes-instance. The same scheme of the algorithms can be applied to a wider class of graphs, $K_{3,t}$-free graphs for any fixed integer $t ge 3$, and it yields fixed-parameter algorithms." @default.
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- W2949880204 date "2014-06-25" @default.
- W2949880204 modified "2023-10-18" @default.
- W2949880204 title "Fixed-Parameter Tractability of Token Jumping on Planar Graphs" @default.
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- W2949880204 doi "https://doi.org/10.48550/arxiv.1406.6567" @default.
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