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

TL;DR

This paper addresses the problem of optimally placing green bridges in networks to reconnect fragmented habitats for wildlife, focusing on computational complexity and algorithms for specific graph classes and habitat sizes.

Contribution

It introduces the problem of habitat connectivity via green bridges, analyzing its complexity and providing algorithms and hardness results for various graph scenarios.

Findings

Efficient algorithms for small habitats on planar graphs.

NP-hardness results for general graphs with larger habitats.

Complexity varies with habitat size and graph properties.

Abstract

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 $\Delta$. We provide efficient algorithms and NP-hardness results for different values of $\Delta$ and maximum habitat sizes on general and planar graphs.