Planar Disjoint-Paths Completion

Disjoint Paths in Planar Graphs

ACKNOWLEDGEMENTS My thanks first to my advisor, Xingxing Yu. He has helped me find my strengths, and directed me toward questions which truly intrigue me. He kept me moving forward in moments of frustration, set high expectations, and provided support for me to meet them. their service on my thesis committee. I would also like to thank Robin Thomas and the rest of the faculty at Georgia Tech fo...

Vertex Disjoint Paths in Upward Planar Graphs

The k-vertex disjoint paths problem is one of the most studied problems in algorithmic graph theory. In 1994, Schrijver proved that the problem can be solved in polynomial time for every fixed k when restricted to the class of planar digraphs and it was a long standing open question whether it is fixed-parameter tractable (with respect to parameter k) on this restricted class. Only recently, [1...

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.

Length-bounded disjoint paths in planar graphs

On Shortest Disjoint Paths in Planar Graphs

For a graph G and a collection of vertex pairs {(s1, t1), . . . , (sk, tk)}, the k disjoint paths problem is to find k vertex-disjoint paths P1, . . . , Pk, where Pi is a path from si to ti for each i = 1, . . . , k. In the corresponding optimization problem, the shortest disjoint paths problem, the vertex-disjoint paths Pi have to be chosen such that a given objective function is minimized. We...