# Multilayer Backbones for Internet of Battlefield Things +
## 1 Introduction
### Related Literature  
The Internet of Battlefield Things concept emerged some five years ago [1; 4], and since then research is conducted in designing backbones [5; 6], in designing reconfigurable and secure IoBT networks [7], in developing solutions for enemy localization [8], in controling/monitoring communication links, in combating attacks at nodes [9], in detecting malware and fake news [10; 11], and in protecting human assets [12; 13].  
The past literature on designing backbones for routing support in wireless ad hoc networks comprises the most closely related work to the present article. This literature is literally enormous during the past two decades [14; 15; 16]. However, the same issue in the realm of military/IoBT networks is different; these networks are actually multilayer networks [5; 7] (see Figure 1), and therefore this past literature is in principle inappropriate, because it concentrates only on single layer networks. Moreover, we showed in ([5] Theorem 1), that these algorithms usually produce suboptimal solutions in the sense that, instead of announcing as a dominator a node with a few interlayer links, they tend to announce someone with many intralayer links. Finally, the work in [17] deals with domination in multiplex networks which is a far more restricted version of multilayer networks, since interlayer links exist only between _clones_ of the same node in different layers; moreover, that work does not establish the computational complexity of their problem.  
The very first algorithm for calculating a backbone for multilayer military networks is described in [5], where a distributed backbone establishment algorithm, namely _clPCI_ was presented. It is based on the concept of connected dominating sets (CDS). The concept of a CDS was selected for the following reasons: (a) only/mainly distributed algorithms are appropriate in the battlefield, and despite the fact that finding a Minimum CDS is a NP-complete problem even in the centralized setting, there exist some very efficient distributed algorithms for the problem; (b) the battlefield requires resilient solutions, and fortunately the scientific knowledge on how to build a multi-connected, multi-dominating  
Figure 1: A sample multilayer IoBT ad hoc network.  
CDS is quite mature [18]; and finally (c) an IoBT is composed by many energy-starving devices, and therefore energy-aware solutions (e.g., sleep scheduling) is almost mandatory; again, the theory on how to create multiple dominating sets, i.e., domatic partitions [19] is quite rich. Until before the introduction of _clPCI_ for constructing a connected dominating set in a distributed fashion for multilayer networks, there was no prior work on the topic. This complete lack may be attributed to the mistaken assumption that a multilayer network is equivalent (from the perspective of computing a CDS) to a single layer network after ignoring layer information.  
Multilayer networks have also been used in biological sciences in order to model interacting networks. In [20], _FAST-MDSM_ is developed to calculate a dominating sets in multilayer networks. However, this algorithm is _centralized_, and it results in an _unconnected_ dominating set, incurring also a high computation cost because it runs as an integer programming problem (Calculating a minimum (connected) dominating set after formulating it as an integer programming model is a mature technique [21]). In conclusion, all aforementioned algorithms consider only single layer networks, with the exception of [5], and of the centralized _FAST-MDSM_ which comprises a departure from this literature.