The complexity landscape of disaster‐aware network extension problems

Abstract

AbstractThis article deals with the complexity of problems related to finding cost‐efficient, disaster‐aware cable routes. We overview various mathematical problems studied to augment a backbone network topology to make it more robust against regional failures. These problems either consider adding a single cable, multiple cables, or even nodes too. They adapt simplistic or more sophisticated regional failure models. Their objective is to identify the network's weak points or minimize the investment cost concerning the risk of a network outage. We investigate the tradeoffs in mathematical modeling for the same real‐world scenario, where more sophisticated models face more computationally challenging problems. We have seen how efficiently computational geometry algorithms can be used to solve simplified problems even for sufficiently large networks. In this article, we aim to understand why different mathematical models formulated for the same real‐world scenario can or cannot be solved efficiently. In particular, we show simplistic mathematical models that formulate NP‐hard problems.