Multiple-source shortest paths in planar graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Route recovery in vertex-disjoint multipath routing for many-to-one sensor networks
Proceedings of the 9th ACM international symposium on Mobile ad hoc networking and computing
Linear-time algorithms for max flow and multiple-source shortest paths in unit-weight planar graphs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We consider the problem of finding a maximum collection of vertex-disjoint paths in undirected, planar graphs from a vertex $s$ to a vertex $t$. This problem is usually solved using flow techniques, which lead to ${\cal O}(nk)$ and ${\cal O}(n\sqrt{n})$ running times, respectively, where $n$ is the number of vertices and $k$ the maximum number of vertex-disjoint $(s,t)$-paths. The best previously known algorithm is based on a divide-and-conquer approach and has running time ${\cal O}(n\log n)$. The approach presented here is completely different from these methods and yields a linear-time algorithm.