### Interference-Aware Broadcast Scheduling in Wireless Networks

Gruia Calinescu, Sutep Tongngam
2008 2008 The 4th International Conference on Mobile Ad-hoc and Sensor Networks
In this paper, we study the I-A B S problem, where all nodes in the Euclidean plane have a transmission range and an interference range equal to r and αr for α ≥ 1, respectively. Minimizing latency is known to be NP-Hard even when α = 1. The network radius D, the maximum graph distance from the source to any node, is also known to be a lower bound. We formulate the problem as Integer Programs (IP) and optimally solve moderate-size instances. We also propose six
more » ... riations of heuristics, which require no pre-processing of inputs, based on the number of receivers gained by each additional simultaneous transmitting node. The experimental results show that the best heuristics give solutions that exceed the optimal solutions by only 13-20%. the optimum solutions. Further, an O(αD) schedule is proven to exist yielding an O(α) approximation algorithm. Previous work The Euclidean model is used when identical nodes in the network can be represented as points in the Euclidean plane and the distance between two nodes is denoted by the Euclidean distance. We normalize the distances such that the transmission range is 1. The communication graph of an instance is a special type of graph called unit disk graph (UDG). By defining the collision and interference as at least two neighbors of node v transmit packets at the same time, i.e., α = 1, Gandhi et al. prove in (10) that finding a minimum-latency broadcast schedule with the collision constraint is NP-Hard in the Euclidean model. They also propose a distributed C-F B S algorithm with latency O(D), where D is the radius of the communication graph. The graph radius D is defined as the maximum graph distance from the source of the broadcast. Thus D is the depth of the BFS tree rooted at the source. S.C.-H. Huang et al. propose three progressively improved approximation algorithms for the same problem, also in the Euclidean model. Their centralized algorithms are based on connected dominating set, k-independent set, and node coloring of the input graph. They claim in (11) that their algorithms produce broadcast schedules with latency at most 24D − 23, 16D − 15, and D + O(log D). In a distributed setting, Emek et al. (12) obtain matching upper and lower bounds of Θ(min(D+ g 2 , D log g)), where g, called the granularity of the network, is the inverse of the minimum dis-2