The high-level contribution of this paper is to establish benchmarks for the minimum hop count per source-receiver path and the minimum number of edges per tree for multicast routing in mobile ad hoc networks (MANETs) under different mobility models. In this pursuit, we explore the tradeoffs between these two routing strategies with respect to hop count, number of edges and lifetime per multicast tree with respect to the Random Waypoint, City Section and Manhattan mobility models. We employ the Breadth First Search algorithm and the Minimum Steiner Tree heuristic for determining a sequence of minimum hop and minimum edge trees respectively. While both the minimum hop and minimum edge trees exist for a relatively longer time under the Manhattan mobility model; the number of edges per tree and the hop count per source-receiver path are relatively low under the Random Waypoint model. For all the three mobility models, the minimum edge trees have a longer lifetime compared to the minimum hop trees and the difference in lifetime increases with increase in network density and/or the multicast group size. Multicast trees determined under the City Section model incur fewer edges and lower hop count compared to the Manhattan mobility model.
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