Coordinated motion planning minimizing total travel length is FPT parameterized by k on graphs arising from discretizations of simple polygons.
Kolliopoulos, Philipp Klaus Krause, Daniel Lokshtanov, Saket Saurabh, and Dimitrios M
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A decomposition-based framework finds entire sets of irrelevant vertices in linear time on bounded-genus graphs, enabling linear-time algorithms for minor containment, disjoint paths, and deletion problems.
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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.