Finding Disjoint Paths on Directed Acyclic Graphs
نویسنده
چکیده
Given k + 1 pairs of vertices (s1, s2), (u1, v1), . . . , (uk, vk) of a directed acyclic graph, we show that a modified version of a data structure of Suurballe and Tarjan can output, for each pair (ul, vl) with 1 ≤ l ≤ k, a tuple (s1, t1, s2, t2) with {t1, t2} = {ul, vl} in constant time such that there are two disjoint paths p1, from s1 to t1, and p2, from s2 to t2, if such a tuple exists. Disjoint can mean vertexas well as edge-disjoint. As an application we show that the presented data structure can be used to improve the previous best known running time O(mn) for the so called 2-disjoint paths problem on directed acyclic graphs to O(m log2+m/n n + n log 3 n). In this problem, given four vertices s1, s2, t1, and t2, we want to construct two disjoint paths p1, from s1 to t1, and p2, from s2 to t2, if such paths exist.
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تاریخ انتشار 2005