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Non-Crossing Shortest Paths in Undirected Unweighted Planar Graphs in Linear Time (2102.10892v2)
Published 22 Feb 2021 in cs.DS
Abstract: Given a set of well-formed terminal pairs on the external face of an undirected planar graph with unit edge weights, we give a linear-time algorithm for computing the union of non-crossing shortest paths joining each terminal pair, where well-formed means that such a set of non-crossing paths exists. This allows us to compute distances between each terminal pair, within the same time bound. We also give a novel concept of incremental shortest path subgraph of a planar graph, i.e., a partition of the planar embedding in subregions that preserve distances, that can be of interest itself.
- Lorenzo Balzotti (8 papers)
- Paolo G. Franciosa (7 papers)