Virtual coordinate system using dominating set for GPS-free adhoc networks

Abstract

Reported work on virtual coordinate assignment (VCA) schemes are iterative-based techniques which rely upon geometric projection (i.e., projecting on circle) or embedding of network topology to low-dimensional Euclidean space (like graph embedding, multidimensional scaling). The performance of existing VCA techniques is constrained by topological situations such as low density or having voids/holes, where greedy forwarding suffers due to local minima when no neighbor is found closer to the destination or low-quality routes comprised of long distance hops. Another drawback of existing VCA techniques is the requirement of thousand iterations for usable coordinate convergence. In order to overcome these drawbacks, we propose a novel virtual coordinate construction technique using graph-theoretic dominating sets. Dominating set (DS) of G is a subset of vertices such that each vertex in G is either in DS or has a neighbor in DS. We found that our virtual coordinate assignment using dominating set algorithm has an approximation ratio $((4.8+\ln 5)opt +1.2)$, where opt is the minimum size dominating set which has the same approximation ratio as minimum dominating set problem. Our algorithm has time complexity $\mathcal {O}(n)$ times and $\mathcal {O}(D)$ rounds and message complexity is $\mathcal {O}(n\log n)$, where D is the radius and n is the number of nodes in networks.