Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Robust capacitated trees and networks with uniform demands *

Abstract : 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 covering the root and the terminals: we give complexity results and propose models to optimize both the cost of the tree and the number of terminals disconnected from the root in the worst case of an edge failure, while respecting the capacity constraints on the edges. Second, we consider the problem of computing a minimum-cost survivable network, i.e., a network that covers the root and terminals even after the removal of any k edges, while still respecting the capacity constraints on the edges. We also consider the possibility of protecting a given number of edges. We propose three different formulations: a cut-set based formulation, a flow based one, and a bilevel one (with an attacker and a defender). We propose algorithms to solve each formulation and compare their efficiency.
Complete list of metadatas

Cited literature [19 references]  Display  Hide  Download
Contributor : Thomas Ridremont <>
Submitted on : Friday, January 12, 2018 - 4:40:40 PM
Last modification on : Friday, August 21, 2020 - 1:56:05 PM


Files produced by the author(s)


  • HAL Id : hal-01681373, version 1
  • ARXIV : 1801.04696


Cédric Bentz, Marie-Christine Costa, Pierre-Louis Poirion, Thomas Ridremont. Robust capacitated trees and networks with uniform demands *. 2018. ⟨hal-01681373⟩



Record views


Files downloads