Parameterized Complexities of Dominating and Independent Set Reconfiguration
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We settle the parameterized complexities of several variants of independent set reconfiguration and dominating set reconfiguration, parameterized by the number of tokens. We show that both problems are XL-complete when there is no limit on the number of moves and XNL-complete when a maximum length ℓ for the sequence is given in binary in the input. The problems are known to be XNLP-complete when ℓ is given in unary instead, and W[1]- and W[2]-hard respectively when ℓ is also a parameter. We complete the picture by showing membership in those classes. Moreover, we show that for all the variants that we consider, token sliding and token jumping are equivalent under pl-reductions. We introduce partitioned variants of token jumping and token sliding, and give pl-reductions between the four variants that have precise control over the number of tokens and the length of the reconfiguration sequence.
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