## 2 Related Works
### Area Coverage Optimization Approaches  
Many optimization approaches have been proposed for area coverage problems. Among them, some explore the movement-assisted sensor node deployment by using mobile nodes to improve coverage quality [7; 8; 9; 10; 11; 12], and these approaches are only suitable to the scenario where the sensor node is omnidirectional. In Ref. [7], the authors propose a virtual force algorithm as a sensor deployment strategy to enhance the coverage after an initial random placement of sensor nodes. In Ref. [8], a localized scan-based movement-assisted sensor deployment method is proposed to use scan and dimension exchange to achieve a balanced state. To address another coverage problem, authors in Ref. [9] propose the optimal coverage in directional sensor networks problem to cover maximal area while activating as few as sensor nodes as possible. To study how to place mobile sensor nodes to get high coverage, Ref. [10] designs two sets of distributed approaches for controlling the movement of sensor nodes. In Ref. [11], the authorspropose a harmony search optimization algorithm to solve area coverage problem. A previous study in Ref. [12] proposes a learning automata-based heuristic algorithm to find a near optimal solution to the proxy equivalent degree-constrained minimum-weight extension of the connected dominating set problem. With the increasing application of surveillance camera and video sensing network, some approaches for directional sensor networks have been proposed. Some consider both the rotation and movement of sensor nodes [13; 14; 15; 16; 17; 18], and the others only consider the rotation of static sensor nodes [19; 20; 21; 22]. Ref. [13] proposes a moving algorithm based on virtual forces of directional sensor nodes to eliminate coverage holes. In Ref. [14], the authors present distributed self-deployment schemes of mobile sensor node according to the circumcenter and incenter of sensing direction. Taking another perspective on the coverage problem, authors in Ref. [15] propose two Enahanced Deployment algorithms namly EDA-1 and EDA-2 to maximize coverage ratio for heterogeneous directional mobile network. To address the deployment problem, authors in Refs. [16; 17] transform the area coverage problem into cell coverage problems by exploiting the Voronoi diagram. Ref. [16] proposes a distributed approach to enhance the overall area coverage, and Ref. [17] presents three local coverage optimization algorithm to improve coverage ratio. Different from above two approaches, Ref. [18] presents several coverage increment algorithms namely vertex-based adjustment with Voronoi diagram (V-VD), edge-based adjustment with Voronoi diagram (E-VD), edge-based adjustment with Delaunay triangulation (E-DT) and angle-based adjustment with Delaunay triangulation (A-DT). Authors in Ref. [19] introduce the concept of sensing centroid into an omni-directional one, and the artificial fish-swarm algorithm is utilized to reduce the coverage hole and achieve the global coverage optimization. In Ref. [20], the proposed approach studies how many sensor nodes are needed to meet a given required coverage probability under the circumstance that the sensing radius is adjustable. However, these two approaches ignore the redundancy ratio which is also a vital factor for improving coverage quality. In Refs. [21; 22], the coverage ratio and redundancy ratio are considered at the same time. Among those, Ref. [21] proposes a virtual potential field based coverage algorithm to increase the coverage ratio by forcing sensor nodes to turn form overlapping region to coverage holes after random deployment. In Ref. [22], a virtual centripetal force-based coverage-enhancing algorithm is proposed to enhance the coverage by redeploying sensor nodes under the repel force-based centripetal force to shut off redundant nodes. However, these two approaches consider that coverage ratio and redundancy ratio have a negative correlation, and they are not suitable to the scenario where the target area is multiply covered.