Localized construction of bounded degree and planar spanner for wireless ad hoc networks

We propose a novel localized algorithm that constructs a bounded degree and planar spanner for wireless ad hoc networks modeled by unit disk graph (UDG). Every node only has to know its 2-hop neighbors to find the edges in this new structure. Our method applies the Yao structure on the local Delaunay graph [21] in an ordering that are computed locally. This new structure has the following attractive properties: (1) it is a planar graph; (2) its node degree is bounded from above by a positive constant 19 + 2π α ; (3) it is a t-spanner (given any two nodes u and v, there is a path connecting them in the structure such that its length is no more than t ≤ max{π 2 , π sin α 2 +1}·Cdel times of the shortest path in UDG); (4) it can be constructed locally and is easy to maintain when the nodes move around; (5) moreover, we show that the total communication cost is O(n), where n is the number of wireless nodes, and the computation cost of each node is at most O(d log d), where d is i...

• Type: Conference
• Year: 2003
• Where: DIALM
• Authors: Yu Wang 0003, Xiang-Yang Li
• Keywords: DIALM 2003, Planar Spanner, Unit Disk Graph, Wireless Ad Hoc Networks