Placing Green Bridges Optimally, with Habitats Inducing Cycles

TL;DR

This paper investigates the optimal placement of green bridges to connect fragmented habitats, analyzing the problem's complexity, proposing efficient algorithms for specific cases, and empirically comparing solution methods.

Contribution

It provides a complexity analysis of the habitat connectivity problem, introduces efficient algorithms for special cases, and evaluates multiple solution approaches empirically.

Findings

NP-hardness persists even with habitat-induced cycles

Efficient algorithms exist when habitats induce faces in plane graphs

Approximation algorithms perform well in practice

Abstract

Choosing the placement of wildlife crossings (i.e., green bridges) to reconnect animal species' fragmented habitats is among the 17 goals towards sustainable development by the UN. We consider the following established model: Given a graph whose vertices represent the fragmented habitat areas and whose weighted edges represent possible green bridge locations, as well as the habitable vertex set for each species, find the cheapest set of edges such that each species' habitat is connected. We study this problem from a theoretical (algorithms and complexity) and an experimental perspective, while focusing on the case where habitats induce cycles. We prove that the NP-hardness persists in this case even if the graph structure is restricted. If the habitats additionally induce faces in plane graphs however, the problem becomes efficiently solvable. In our empirical evaluation we compare this algorithm as well as ILP formulations for more general variants and an approximation algorithm with another. Our evaluation underlines that each specialization is beneficial in terms of running time, whereas the approximation provides highly competitive solutions in practice.