Disjoint Paths in Acyclic Digraphs

Disjoint Paths in Symmetric Digraphs

Given a number of requests `, we propose a polynomial-time algorithm for finding ` disjoint paths in a symmetric directed graph. It is known that the problem of finding ` ≥ 2 disjoint paths in a directed graph is NP-hard [S. Fortune, J. Hopcroft, J. Wyllie, The directed subgraph homeomorphism problem, Journal of Theoretical Computer Science 10 (2) (1980) 111–121]. However, by studying minimal s...

Arc-Disjoint Paths in Expander Digraphs

Arc-Disjoint Paths in Decomposable Digraphs

4 We prove that the weak k-linkage problem is polynomial for every fixed k for totally Φ5 decomposable digraphs, under appropriate hypothesis on Φ. We then apply this and recent results 6 by Fradkin and Seymour (on the weak k-linkage problem for digraphs of bounded independence 7 number or bounded cut-width) to get polynomial algorithms for some class of digraphs like quasi8 transitive digraphs...

On disjoint paths in acyclic planar graphs

We give an algorithm with complexity O(f(R) 2 kn) for the integer multiflow problem on instances (G,H, r, c) with G an acyclic planar digraph and r + c Eulerian. Here, f is a polynomial function, n = |V (G)|, k = |E(H)| and R is the maximum request maxh∈E(H) r(h). When k is fixed, this gives a polynomial algorithm for the arc-disjoint paths problem under the same hypothesis.

Finding Disjoint Paths on Directed Acyclic Graphs

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. Di...