Coordinated motion planning minimizing total travel length is FPT parameterized by k on graphs arising from discretizations of simple polygons.
21 Jörg Flum and Martin Grohe.Parameterized Complexity Theory, volume XIV ofTexts in Theoretical Computer Science
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Coordinated Motion Planning is FPT on Discretized Simple Polygons
Coordinated motion planning minimizing total travel length is FPT parameterized by k on graphs arising from discretizations of simple polygons.