An Efficient Search Algorithm for Multi-hop Network Localization in a Sparse Unit Disk Graph Model

Abstract

We consider a network localization problem by modeling this as a unit disk graph where nodes are randomly placed with uniform distribution in an area.The connectivity between nodes is defined when the distances fall within a unit range. Under a condition that certain nodes know their locations (anchor nodes), this paper proposes a heuristic approach to find a realization for the rest of the network by applying a tree search algorithm in a depth- first search manner. Our contribution is to put together a priori information and constraints such as graph properties in order to speed up the search. An evaluation function is formed and used to prune down the search space. This evaluation function is used to select the order of the unknown nodes to iterate. This paper also extends the idea further by accommodating a variety of other properties of graphs into the evaluation function. The results show that node degrees, node distances and shortest paths to anchor nodes drastically reduce the number of iterations required for realizing a feasible localization instance both in noise-free and noisy environments. Finally, some preliminary complexity analysis is also given.