On approximation algorithms and the cost of decentralization for problems in network restoration

Abstract

In this dissertation project, we investigate approximation algorithms and the cost of decentralized decision-making arising from problems in post-disaster infrastructure network restoration. Problems arising both in single infrastructure network restoration and multi-infrastructure network restoration are investigated.

In the area of single infrastructure restoration, we investigate a fractional optimization problem arising in dispatching rules for Integrated Network Design and Scheduling (INDS) problems. We demonstrate the NP-hardness for the fractional optimization and provide tight approximation guarantees for the dispatching rules.

Despite the wide existence of interdependencies, post-disaster restoration efforts for interdependent multi-infrastructure systems are often made in a decentralized manner as each infrastructure sets their individual work schedule towards its own best performance. We examine Algorithmic Game Theory and develop Decentralized Interdependent Scheduling (DIS) framework to model these interactions between infrastructures and to quantify the impacts of decentralization using the price of anarchy (PoA) and the price of stability (PoS). Upper bounds for the PoA and the PoS are demonstrated to depend linearly on the sum of the processing times of the restoration tasks across the system. Mixed integer program constraints are formulated to characterize Nash equilibria and an incentive structure for Incomplete Information Simple External Dependency DIS Games (iSEDGs). In numerical experiments, the constraints are used to evaluate the PoA and the PoS for iSEDGs, their upper bounds and improved PoS under incentive structure. In many cases, the PoA and the PoS could be improved by incentivizing players with external fund.