Maximization Versions of “ Lights Out ” Games in Grids and Graphs

  title={Maximization Versions of “ Lights Out ” Games in Grids and Graphs},
  author={John Goldwasser and William Klostermeyer},
Complexity results and algorithms are given for the problem of maximizing the number of off vertices (switches) in graphs and m×n rectangular grids. When a switch is toggled, it and its neighbors change state. It is shown that the problem is NP-complete in graphs and a simple approximation algorithm is given as well as a nonapproximability result. Fixed-parameter problems are studied in grids and graphs and an algorithm given for m × n grids that turn at least mn − m 2 vertices off, m ≤ n. It… CONTINUE READING