Underwater wireless sensor networks (UWSNs) are a promising technology to provide oceanographers with environmental data
in real time. Suitable network topologies to monitor estuaries are formed by strings coming together to a sink node.This network
may be understood as an oriented graph. A number of MAC techniques can be used in UWSNs, but Spatial-TDMA is preferred
for fixed networks. In this paper, a scheduling procedure to obtain the optimal fair frame is presented, under ideal conditions
of synchronization and transmission errors. The main objective is to find the theoretical maximum throughput by overlapping
the transmissions of the nodes while keeping a balanced received data rate from each sensor, regardless of its location in the
network. The procedure searches for all cliques of the compatibility matrix of the network graph and solves a Multiple-Vector
Bin Packing (MVBP) problem. This work addresses the optimization problem and provides analytical and numerical results for
both the minimum frame length and the maximum achievable throughput.
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