Topology control is one of the most essential technologies in wireless sensor networks (WSNs); it constructs networks with certain characteristics through the usage of some approaches, such as power control and channel assignment, thereby reducing the inter-nodes interference and the energy consumption of the network. It is closely related to the efficiency of upper layer protocols, especially MAC and routing protocols, which are the same as underwater acoustic sensor networks (UASNs). Directional antenna technology (directional transducer in UASNs) has great advantages in minimizing interference and conserving energy by restraining the beamforming range. It enables nodes to communicate with only intended neighbors; nevertheless, additional problems emerge, such as how to guarantee the connectivity of the network. This paper focuses on the connectivity problem of UASNs equipped with tri-modal directional transducers, where the orientation of a transducer is stabilized after the network is set up. To efficiently minimize the total network energy consumption under constraint of connectivity, the problem is formulated to a minimum network cost transducer orientation (MNCTO) problem and is provided a reduction from the Hamiltonian path problem in hexagonal grid graphs (HPHGG), which is proved to be NP-complete. Furthermore, a heuristic greedy algorithm is proposed for MNCTO. The simulation evaluation results in a contrast with its omni-mode peer, showing that the proposed algorithm greatly reduces the network energy consumption by up to nearly half on the premise of satisfying connectivity.
Keywords: NP-complete; UASNs; connectivity; directional; topology control.