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). However, 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 is spent in learning the existing code modules of the simulator and the logical flow between the different code modules. The purpose of this chapter is to illustrate the applications of Graph Theory algorithms to study, analyze, and simulate the behavior of routing protocols for MANETs. Specifically, the chapter focuses 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). The chapter discusses 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.
All-pairs bottleneck paths for general graphs in truly sub-cubic time