Network recovery from massive failures under uncertain knowledge of damages

This paper addresses progressive network recovery under uncertain knowledge of damages. We formulate the problem as a mixed integer linear programming (MILP), and show that it is NP-Hard. We propose an iterative stochastic recovery algorithm (ISR) to recover the network in a progressive manner to satisfy the critical services. At each optimization step, we make a decision to repair a part of the network and gather more information iteratively, until critical services are completely restored. Three different algorithms are used to find a feasible set and determine which node to repair, namely, 1) an iterative shortest path algorithm (ISR-SRT), 2) an approximate branch and bound (ISR-BB) and 3) an iterative multi-commodity LP relaxation (ISR-MULT). Further, we have modified the state-of-the-Art iterative split and prune (ISP) algorithm to incorporate the uncertain failures. Our results show that ISR-BB and ISR- MULT outperform the state-of-the-Art 'progressive ISP' algorithm while we can configure our choice of trade-off between the execution time, number of repairs (cost) and the demand loss. We show that our recovery algorithm, on average, can reduce the total number of repairs by a factor of about 3 with respect to ISP, while satisfying all critical deman

On Fundamental Bounds on Failure Identifiability by Boolean Network Tomography

Boolean network tomography is a powerful tool to infer the state (working/failed) of individual nodes from path-level measurements obtained by edge-nodes. We consider the problem of optimizing the capability of identifying network failures through the design of monitoring schemes. Finding an optimal solution is NP-hard and a large body of work has been devoted to heuristic approaches providing lower bounds. Unlike previous works, we provide upper bounds on the maximum number of identifiable nodes, given the number of monitoring paths and different constraints on the network topology, the routing scheme, and the maximum path length. These upper bounds represent a fundamental limit on identifiability of failures via Boolean network tomography. Our analysis provides insights on how to design topologies and related monitoring schemes to achieve the maximum identifiability under various network settings. Through analysis and experiments we demonstrate the tightness of the bounds and efficacy of the design insights for engineered as well as real networks