Cuts and Disjoint Paths in the Valley-Free Path Model

Cuts and Disjoint Paths in the Valley-Free Path Model of Internet BGP Routing

In the valley-free path model, a path in a given directed graph is valid if it consists of a sequence of forward edges followed by a sequence of backward edges. This model is motivated by BGP routing policies of autonomous systems in the Internet. Robustness considerations lead to the problem of computing a maximum number of disjoint paths between two nodes, and the minimum size of a cut that s...

Induced Disjoint Paths in Claw-Free Graphs

Paths P1, . . . , Pk in a graph G = (V,E) are said to be mutually induced if for any 1 ≤ i < j ≤ k, Pi and Pj have neither common vertices nor adjacent vertices (except perhaps their end-vertices). The Induced Disjoint Paths problem is to test whether a graph G with k pairs of specified vertices (si, ti) contains k mutually induced paths Pi such that Pi connects si and ti for i = 1, . . . , k. ...

The Disjoint Paths Problem

Disjoint Paths in Metacube

A new interconnection network with low-degree for very large parallel computers called metacube (MC) has been introduced recently. The MC network has short diameter similar to that of the hypercube. However, the degree of an MC network is much lower than that of a hypercube of the same size. More than one hundred of millions of nodes can be connected by an MC network with up to 6 links per node...

Disjoint paths in arborescences

An arborescence in a digraph is a tree directed away from its root. A classical theorem of Edmonds characterizes which digraphs have λ arc-disjoint arborescences rooted at r. A similar theorem of Menger guarantees λ strongly arc disjoint rv-paths for every vertex v, where “strongly” means no two paths contain a pair of symmetric arcs. We prove that if a directed graph D contains two arc-disjoin...