  Broadcast is a fundamental network operation, widely used in wireless
networks to disseminate messages. The energy-efficiency of broadcast is
important particularly when devices in the network are energy constrained. To
improve the efficiency of broadcast, different approaches have been taken in
the literature. One of these approaches is broadcast with energy accumulation.
Through simulations, it has been shown in the literature that broadcast with
energy accumulation can result in energy saving. The amount of this saving,
however, has only been analyzed for linear multi-hop wireless networks. In this
work, we extend this analysis to two-dimensional (2D) multi-hop networks. The
analysis of saving in 2D networks is much more challenging than that in linear
networks. It is because, unlike in linear networks, in 2D networks, finding
minimum-energy broadcasts with or without energy accumulation are both NP-hard
problems. Nevertheless, using a novel approach, we prove that this saving is
constant when the path loss exponent alpha is strictly greater than two. Also,
we prove that the saving is theta(log n) when alpha=2, where n denotes the
number of nodes in the network.
