Shortest Path Separators in Unit Disk Graphs

Elfarouk Harb, Zhengcheng Huang, Da Wei Zheng

Abstract:

We introduce a new balanced separator theorem for unit-disk graphs involving two shortest paths
combined with the 1-hop neighbours of those paths and two other vertices. This answers an open
problem of Yan, Xiang and Dragan [CGTA ’12] and improves their result that requires removing the
3-hop neighbourhood of two shortest paths. Our proof uses very different ideas, including Delaunay
triangulations and a generalization of the celebrated balanced separator theorem of Lipton and
Tarjan [J. Appl. Math. ’79] to systems of non-intersecting paths.