Reconfigurable intelligent surfaces (RISs) are expected to make future 6G
networks more connected and resilient against node failures, due to their
ability to introduce controllable phase-shifts onto impinging electromagnetic
waves and impose link redundancy. Meanwhile, unmanned aerial vehicles (UAVs)
are prone to failure due to limited energy, random failures, or targeted
failures, which causes network disintegration that results in information
delivery loss. In this paper, we show that the integration between UAVs and
RISs for improving network connectivity is crucial. We utilize RISs to provide
path diversity and alternative connectivity options for information flow from
user equipments (UEs) to less critical UAVs by adding more links to the
network, thereby making the network more resilient and connected. To that end,
we first define the criticality of UAV nodes, which reflects the importance of
some nodes over other nodes. We then employ the algebraic connectivity metric,
which is adjusted by the reflected links of the RISs and their criticality
weights, to formulate the problem of maximizing the network connectivity. Such
problem is a computationally expensive combinatorial optimization. To tackle
this problem, we propose a relaxation method such that the discrete scheduling
constraint of the problem is relaxed and becomes continuous. Leveraging this,
we propose two efficient solutions, namely semi-definite programming (SDP)
optimization and perturbation heuristic, which both solve the problem in
polynomial time. For the perturbation heuristic, we derive the lower and upper
bounds of the algebraic connectivity obtained by adding new links to the
network. Finally, we corroborate the effectiveness of the proposed solutions
through extensive simulation experiments.Comment: 14 pages, 8 figures, journal paper. arXiv admin note: text overlap
with arXiv:2308.0467