Removing Connected Obstacles in the Plane Is FPT

Authors Eduard Eiben , Daniel Lokshtanov

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Author Details

Eduard Eiben
  • Department of Computer Science, Royal Holloway, University of London, UK
Daniel Lokshtanov
  • Department of Computer Science, UC Santa Barbara, CA, USA

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Eduard Eiben and Daniel Lokshtanov. Removing Connected Obstacles in the Plane Is FPT. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 39:1-39:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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 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 (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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Computational geometry
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Graph algorithms analysis
  • parameterized complexity and algorithms
  • planar graphs
  • motion planning
  • barrier coverage
  • barrier resilience
  • colored path
  • minimum constraint removal


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