Graph Theory Algorithms for Mobile Ad Hoc Networks

Various simulators (e.g., ns-2 and GloMoSim) are available to implement and study the behavior of the routing protocols for mobile ad hoc networks (MANETs). But, students and investigators who are new to this area often get perplexed in the complexity of these simulators and lose the focus in designing and analyzing the characteristics of the network and the protocol. Most of the time would be spent in learning the existing code modules of the simulator and the logical flow between the different code modules. The purpose of this paper would be to illustrate the applications of Graph Theory algorithms to study, analyze and simulate the behavior of routing protocols for MANETs. Specifically, we focus on the applications of Graph Theory algorithms to determine paths, trees and connected dominating sets for simulating and analyzing respectively unicast (single-path and multi-path), multicast and broadcast communication in mobile ad hoc networks (MANETs). We will discuss the (i) Dijkstra's shortest path algorithm and its modifications for finding stable paths and bottleneck paths; (ii) Prim's minimum spanning tree algorithm and its modification for finding all pairs smallest and largest bottleneck paths; (iii) Minimum Steiner tree algorithm to connect a source node to all the receivers of a multicast group; (iv) A node-degree based algorithm to construct an approximate minimum connected dominating set (CDS) for sending information from one node to all other nodes in the network; and (v) Algorithms to find a sequence of link-disjoint, node-disjoint and zone-disjoint multi-path routes in MANETs.