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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

## Abstract

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.

Original language English 33rd International Symposium on Algorithms and Computation, ISAAC 2022 Sang Won Bae, Heejin Park Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing 9783959772587 https://doi.org/10.4230/LIPIcs.ISAAC.2022.34 Published - 1 Dec 2022 Yes 33rd International Symposium on Algorithms and Computation, ISAAC 2022 - Virtual, Online, Korea, Republic ofDuration: 19 Dec 2022 → 21 Dec 2022

### Publication series

Name Leibniz International Proceedings in Informatics, LIPIcs 248 1868-8969

### Conference

Conference 33rd International Symposium on Algorithms and Computation, ISAAC 2022 Korea, Republic of Virtual, Online 19/12/22 → 21/12/22

## Keywords

• computational geometry
• polygon nesting
• polygon separation

• Software

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