Minimum Link Fencing

Authors Sujoy Bhore , Fabian Klute , Maarten Löffler, Martin Nöllenburg , Soeren Terziadis , Anaïs Villedieu

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Author Details

Sujoy Bhore
  • Department of Computer Science & Engineering, Indian Institute of Technology Bombay, India
Fabian Klute
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
Maarten Löffler
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
Martin Nöllenburg
  • Algorithms and Complexity Group, TU Wien, Austria
Soeren Terziadis
  • Algorithms and Complexity Group, TU Wien, Austria
Anaïs Villedieu
  • Algorithms and Complexity Group, TU Wien, Austria


The authors would like to thank Thekla Hamm and Irene Parada for the valuable discussion in particular concerning the XP results of Section 3.

Cite AsGet BibTex

Sujoy Bhore, Fabian Klute, Maarten Löffler, Martin Nöllenburg, Soeren Terziadis, and Anaïs Villedieu. Minimum Link Fencing. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 34:1-34:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We study a variant of the geometric multicut problem, where we are given a set 𝒫 of colored and pairwise interior-disjoint polygons in the plane. The objective is to compute a set of simple closed polygon boundaries (fences) that separate the polygons in such a way that any two polygons that are enclosed by the same fence have the same color, and the total number of links of all fences is minimized. We call this the minimum link fencing (MLF) problem and consider the natural case of bounded minimum link fencing (BMLF), where 𝒫 contains a polygon Q that is unbounded in all directions and can be seen as an outer polygon. We show that BMLF is NP-hard in general and that it is XP-time solvable when each fence contains at most two polygons and the number of segments per fence is the parameter. Finally, we present an O(n log n)-time algorithm for the case that the convex hull of 𝒫⧵{Q} does not intersect Q.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • computational geometry
  • polygon nesting
  • polygon separation


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