Improved Algorithms for the 2-Vertex Disjoint Paths Problem
Given distinct vertices s 1,s 2,t 1, and t 2 the 2-vertex-disjoint paths problem (2-VDPP) consists in determining two vertex-disjoint paths p 1, from s 1 to t 1, and p 2, from s 2 to t 2, if such paths exist.
We show that by using some kind of sparsification technique the previously best known time bound of O(n + mα(m,n)) can be reduced to O(m + nα(n,n)), where α denotes the inverse of the Ackermann function. Moreover, we extend the very practical and simple algorithm of Hagerup for solving the 2-VDPP on 3-connected planar graphs to a simple linear time algorithm for the 2-VDPP on general planar graphs thereby avoiding the computation of planar embeddings or triconnected components.
KeywordsPlanar Graph Linear Time Improve Algorithm Linear Time Algorithm Original Instance
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