A Partial Unit Delaunay Graph with Planar and Spanner for Ad Hoc Wireless Networks

Abstract

This paper proposes a new geometry structure, namely Partial unit Delaunay graph (PuDel), to be as the underlying network topology of Ad hoc wireless networks. PuDel has the following attractive properties: (1) PuDel is a connected subgraph of unit Delaunay triangulation; (2) PuDel is a planar spanner of Unit Disk Graph (UDG) whose length stretch factor is at most 1.21; and (3) PuDel can be locally constructed only based on the position information of 1-hops neighbors, and requires no message exchange between nodes in addition to maintaining UDG.