Parameterized Complexities of Dominating and Independent Set Reconfiguration

Abstract 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, XNL-complete when a maximum length $$\ell $$ ℓ for the sequence is given in binary in the input, and XNLP-complete when $$\ell $$ ℓ is given in unary. The problems were known to be $$\textrm{W}[1]$$ W [ 1 ] - and $$\textrm{W}[2]$$ W [ 2 ] -hard respectively when $$\ell $$ 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…

• EC
  European Commission

  Awards: 853234, 101063180
• NO
  Nederlandse Organisatie voor Wetenschappelijk Onderzoek

  Award: 613.009.031b
• ER
  European Research Council

  Award: 853234