Constructing edge-disjoint Steiner paths in lexicographic product networks

Constructing internally disjoint pendant Steiner trees in Cartesian product networks

The concept of pendant tree-connectivity was introduced by Hager in 1985. For a graph G = (V,E) and a set S ⊆ V (G) of at least two vertices, an S-Steiner tree or a Steiner tree connecting S (or simply, an S-tree) is a subgraph T = (V ′, E ′) of G that is a tree with S ⊆ V ′. For an S-Steiner tree, if the degree of each vertex in S is equal to one, then this tree is called a pendant S-Steiner t...

4.1 Edge Disjoint Paths

Problem Statement: Given a directed graphG and a set of terminal pairs {(s1, t1), (s2, t2), · · · , (sk, tk)}, our goal is to connect as many pairs as possible using non edge intersecting paths. Edge disjoint paths problem is NP-Complete and is closely related to the multicommodity flow problem. In fact integer multicommodity flow is a generalization of this problem. We describe a greedy approx...

Reconstructing edge-disjoint paths

Constructing Node-Disjoint Paths in Enhanced Pyramid Networks

Chen et al. in 2004 proposed a new hierarchy structure, called the enhanced pyramid network (EPM, for short), by replacing each mesh in a pyramid network (PM, for short) with a torus. Recently, some topological properties and communication on the EPMs have been investigated or derived. Their results have revealed that an EPM is an attractive alternative to a PM. This study investigates the node...

Constructing Pairwise Disjoint Paths with

Let P be a simple polygon and let f(ui; u 0 i)g be m pairs of distinct vertices of P where for every distinct i; j m, there exist pairwise disjoint paths connecting ui to u 0 i and uj to u 0 j. We wish to construct m pairwise disjoint paths in the interior of P connecting ui to u 0 i for i = 1; : : : ; m, with minimal total number of line segments. We give an approximation algorithm which in O(...