Flow trees for vertex-capacitated networks

Capacitated vertex covering

In this paper we study the capacitated vertex cover problem, a generalization of the well-known vertex cover problem. Given a graph G = (V ,E) with weights on the vertices, the goal is to cover all the edges by picking a cover of minimum weight from the vertices. When we pick a copy of a vertex, we pay the weight of the vertex and cover up to a pre-specified number of edges incident on this ver...

Flow equivalent trees in undirected node-edge-capacitated planar graphs

Given an edge-capacitated undirected graph G = (V ,E,C) with edge capacity c :E → R+, n = |V |, an s − t edge cut C of G is a minimal subset of edges whose removal from G will separate s from t in the resulting graph, and the capacity sum of the edges in C is the cut value of C. A minimum s − t edge cut is an s − t edge cut with the minimum cut value among all s − t edge cuts. A theorem given b...

Capacitated Trees , Capacitated Routing , and Associated

We study the polyhedral structure of two related core combinatorial problems: the subtree cardinalityconstrained minimal spanning tree problem and the identical customer vehicle routing problem. For each of these problems, and for a forest relaxation of the minimal spanning tree problem, we introduce a number of new valid inequalities and specify conditions for ensuring when these inequalities ...

Vertex Equitable Labelings of Transformed Trees

Robust capacitated trees and networks with uniform demands

We are interested in the design of robust (or resilient) capacitated rooted Steiner networks in case of terminals with uniform demands. Formally, we are given a graph, capacity and cost functions on the edges, a root, a subset of nodes called terminals, and a bound k on the number of edge failures. We first study the problem where k = 1 and the network that we want to design must be a tree cove...