Dangerous graphs

Anomalies and faults are inevitable in computer networks, today more than ever before. This is due to the large scale and dynamic nature of the networks used to process big data and to the ever-increasing number of ad-hoc devices. Beyond natural faults and anomalies occurring in a network, threats proceeding from attacks conducted by malicious intruders must be considered. Consequently, there is often a need to quickly isolate and even repair a fault in a network when it appears. Furthermore, despite the presence in a network of faults stemming from malicious entities, we need to identify the latter and their behaviours, and develop protocols resilient to their attacks. Thus, defining models to capture the dangers inherent to various faults, anomalies and threats in a network and studying such threats, has become increasingly important and popular. Threats in networks can be of two kinds: either mobile or stationary. A malicious mobile process can move along the network, whereas a stationary harmful process resides in a host. One of the most studied models for stationary harmful processes is the black hole, which was introduced by Dobrev, Flocchini, Prencipe and Santoro in 2001. A black hole models a network node in which a destructive process deletes any visiting agent or incoming data upon arrival, without leaving any observable trace. Conversely, a network may face one or more malicious mobile processes infecting one or more nodes. Given both kinds of threats, a first crucial task consists in searching for and reporting as quickly as possible the location all faulty nodes while using a minimum number of mobile agents. In general, the main issue is to identify the minimal hypotheses under which faulty nodes can be found. This problem has been investigated in both asynchronous and synchronous networks. A corollary task is to make sure that the protocols designed for solving problems such as gathering and transferring data still work despite the presence of one or more faulty nodes. In this chapter, we review the state-of-the-art of research pertaining to the presence of faulty nodes in a network. We discuss different models in synchronous and asynchronous networks and for different communication and computation capabilities of the agents. We also address relevant computational issues and present algorithmic techniques and impossibility results