### Abstract

Approximation algorithm for data broadcasting in duty cycled multi-hop wireless networks Dianbo Zhao * and Kwan-Wu Chin Broadcast is a fundamental operation in wireless networks. To this end, many past studies have studied the NP-hard, broadcast problem for always-on multi-hop networks. However, in wireless sensor networks, nodes are powered by batteries, meaning, they have finite energy. Consequently, nodes are required to have a low duty cycle, whereby they switch between active and sleep state periodically. This means that a transmission from a node may not reach all of its neighbors simultaneously. Consequently, any developed broadcast protocols must consider collisions and the wake-up times of neighboring nodes. Henceforth, this paper studies the minimum latency broadcast scheduling problem in duty cycled multi-hop wireless networks (MLBSDC), which remains NP hard. The MLBSDC problem aims to find a collision-free schedule that minimizes the time in which the last node receives a broadcast message. We propose a novel algorithm called CFBS that allows nodes in different layers of the broadcast tree to transmit simultaneously. We prove that CFBS produces a latency of at most (T + 1)H + TO(log2 H). Here, T denotes the number of time slots in a scheduling period, and H is the optimal broadcast latency obtained from the shortest path tree algorithm assuming no collision. We also show that the total number of transmissions is at most 4(T + 2) times larger than the optimal value. The results from extensive simulation show that CFBS has a better performance than OTAB, the best broadcast scheduling algorithm to date. In particular, the broadcast latency achieved by CFBS is up to 320 that of OTAB. 1

### Keyphrases

research open access sleep state optimal value broadcast problem multi-hop wireless network collision-free schedule developed broadcast protocol scheduling period time slot novel algorithm kwan-wu chin broadcast wake-up time paper study fundamental operation broadcast tree multi-hop wireless network dianbo zhao total number approximation algorithm finite energy optimal broadcast latency wireless network path tree wireless sensor network broadcast message minimum latency broadcast scheduling problem different layer broadcast latency many past study low duty cycle extensive simulation show always-on multi-hop network mlbsdc problem