Finding Single-Source Shortest Paths on Planar Graphs with Nonnegative Edge Weights in Linear Time
2020 · A linear-time algorithm for shortest paths in planar graphs.
The need to find shortest paths in a graph from some fixed source vertex to all other vertices is quite obvious and therefore one of the most important problems in graph theory. For general graphs, the standard way to go is the Dijkstra algorithm. On planar graphs, this approach takes linearithmic time in the number of vertices. However, we present an algorithm published by Henzinger et al. in 1997 that accomplishes the task in linear time on planar graphs.