Robust capacitated trees and networks with uniform demands

TL;DR

This paper studies the design of robust capacitated networks with uniform demands, focusing on tree and survivable network structures under edge failure constraints, and proposes models and algorithms for optimization and resilience.

Contribution

It introduces new complexity results, models, and algorithms for designing robust capacitated networks with uniform demands under various failure scenarios.

Findings

Complexity results for k=1 case.

Models optimizing cost and disconnection worst-case.

Algorithms for different network formulations.

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.