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Removing Connected Obstacles in the Plane is FPT (2002.01218v1)
Published 4 Feb 2020 in cs.DS, cs.CG, and cs.DM
Abstract: Given two points in the plane, a set of obstacles defined by closed curves, and an integer $k$, does there exist a path between the two designated points intersecting at most $k$ of the obstacles? This is a fundamental and well-studied problem arising naturally in computational geometry, graph theory, wireless computing, and motion planning. It remains $\textsf{NP}$-hard even when the obstacles are very simple geometric shapes (e.g., unit-length line segments). In this paper, we show that the problem is fixed-parameter tractable ($\textsf{FPT}$) parameterized by $k$, by giving an algorithm with running time $k{O(k3)}n{O(1)}$. Here $n$ is the number connected areas in the plane drawing of all the obstacles.
- Eduard Eiben (54 papers)
- Daniel Lokshtanov (135 papers)