Summary
We exhibit a close relationship between two topics in computational complexity. One topic is the analysis of storage requirements for nondeterministic computations. The corresponding mathematical model is a well known black-white pebble game on directed acyclic graphs. The other topic is the search for small separators of undirected graphs. We model a dynamic version of the concept of a separator with a vertex separator game. This game is closely related to graph layout and searching problems. We show that instances of the black-white pebble game and the vertex separator game can easily be transformed into each other. As an application of this result both games are shown to be NP-complete.
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Lengauer, T. Black-white pebbles and graph separation. Acta Informatica 16, 465–475 (1981). https://doi.org/10.1007/BF00264496
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DOI: https://doi.org/10.1007/BF00264496