A Novel Variable Lie Hypergraph Technique for Cluster Based Routing in Opportunistic Networks.

In recent years, breakneck advancements in technology and the proliferation of wireless handheld devices have drawn tremendous interest to study. An opportunistic network (OppNets) refers to a number of wireless nodes opportunistically communicating with each other which does not rely on any fixed structure. Due to this, routing packets from source to destination in OppNets remain a challenging issue. This paper proposes a multi-objective optimization approach for cluster based routing in OppNets that maximizes average delivery ratio, minimizes both the hop count and average delivery delay. We propose a novel Variable Lie hypergraph theory for a unanimous way of clustering and routing protocol to obtain the optimal solution. A variable hypergraph is constructed by combining the Lie commutator. Variable hyperedges are the clusters, and the variable hypergraph transversal is the required set of cluster heads. Nodes of the variable hyperedges are positioned appropriately in an upper triangular matrix which is an element of upper triangular matrix Lie algebra. Furthermore, we propose the upper triangular routing matrix algorithm that finds the path in identifying the neighbour node by its location inside the upper triangular matrix using Lie commutators. Simulation results using real mobility traces are presented, manifesting the effectiveness of the proposed scheme with very less time.