# The Gain of Energy Accumulation in Multi-hop Wireless Network Broadcast

## TL;DR

This paper analyzes energy savings in multi-hop wireless network broadcasts with energy accumulation, extending previous linear network results to 2D networks and proving constant or logarithmic savings depending on path loss.

## Contribution

It extends the analysis of energy accumulation benefits from linear to 2D networks and proves the savings are constant or logarithmic based on the path loss exponent.

## Key findings

- Energy saving is constant for alpha > 2.
- Energy saving is theta(log n) for alpha = 2.
- Finding minimum-energy broadcasts in 2D is NP-hard.

## Abstract

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.