Placing Green Bridges Optimally, with Close-Range Habitats in Sparse Graphs

Fuente: arXiv
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Main Authors: Wallisch, Christian, Fluschnik, Till, Kellerhals, Leon
Format: Preprint
Published: 2025
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author Wallisch, Christian
Fluschnik, Till
Kellerhals, Leon
author_facet Wallisch, Christian
Fluschnik, Till
Kellerhals, Leon
contents We study a network design problem motivated by the challenge of placing wildlife crossings to reconnect fragmented habitats of animal species, which is among the 17 goals towards sustainable development by the UN: Given a graph, whose vertices represent the fragmented habitat areas and whose edges represent possible green bridge locations (with costs), and the habitable vertex set for each species' habitat, the goal is to find the cheapest set of edges such that each species' habitat is sufficiently connected. We focus on the established variant where a habitat is considered sufficiently connected if it has diameter two in the solution and study its complexity in cases justified by our setting namely small habitat sizes on planar graphs and graphs of small maximum degree $Δ$. We provide efficient algorithms and NP-hardness results for different values of $Δ$ and maximum habitat sizes on general and planar graphs.
format Preprint
id arxiv_https___arxiv_org_abs_2510_21540
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Placing Green Bridges Optimally, with Close-Range Habitats in Sparse Graphs
Wallisch, Christian
Fluschnik, Till
Kellerhals, Leon
Data Structures and Algorithms
Computational Complexity
We study a network design problem motivated by the challenge of placing wildlife crossings to reconnect fragmented habitats of animal species, which is among the 17 goals towards sustainable development by the UN: Given a graph, whose vertices represent the fragmented habitat areas and whose edges represent possible green bridge locations (with costs), and the habitable vertex set for each species' habitat, the goal is to find the cheapest set of edges such that each species' habitat is sufficiently connected. We focus on the established variant where a habitat is considered sufficiently connected if it has diameter two in the solution and study its complexity in cases justified by our setting namely small habitat sizes on planar graphs and graphs of small maximum degree $Δ$. We provide efficient algorithms and NP-hardness results for different values of $Δ$ and maximum habitat sizes on general and planar graphs.
title Placing Green Bridges Optimally, with Close-Range Habitats in Sparse Graphs
topic Data Structures and Algorithms
Computational Complexity
url https://arxiv.org/abs/2510.21540