Mind the Gap: Edge Facility Location Problems in Theory and Practice

Motivated by applications in urban planning, network analysis, and data visualization, we introduce center selection problems in graphs where the centers are represented by edges. This is in contrast to classic center selection problems where centers are usually placed at the nodes of a graph. Given a weighted graph G(V, E) and a budget $$k \in \mathbb {N}$$ , the goal is to select k edges from E such that the maximum distance from any point of interest in the graph to its nearest center is minimized. We consider three different problem variants, based on defining the points of interest either as the edges of G, or the nodes, or all points on the edges. We provide a variety of hardness results and approximation algorithms. A key difficulty of edge center selection is that the underlying distance function may not satisfy the triangle inequality, which is crucially used in approximation algorithms for node center selection. In addition, we introduce efficient heuristics that produce solutions of good quality even in large graphs, as demonstrated in our experimental evaluation.