A Class of Orientation-Invariant Yao-type Subgraphs of a Unit Disk Graph

We introduce a generalization of the Yao graph where the cones used are adaptively centered on a set of nearest neighbors for each node, thus creating a directed or undirected spanning subgraph of a given unit disk graph (UDG). We also permit the apex of the cones to be positioned anywhere along the line segment between the node and its nearest neighbor, leading to a class of Yao-type subgraphs. We show that these locally constructed spanning subgraphs are strongly connected, have bounded out-degree, are t-spanners with bounded stretch factor, contain the Euclidean minimum spanning tree as a subgraph, and are orientationinvariant. Since a continuous set of cone angles are possible, these subgraphs also permit control over the degree of the graph. We demonstrate through simulations that these subgraphs of the UDG combines the desirable properties of the Yao and the Half Space Proximal subgraphs of the UDG.