Minimum-energy broadcasting for cross wireless ad-hoc networks

In this paper, we propose solutions for the minimum-energy broadcasting problem for cross networks, where N nodes are located on two perpendicular lines. Our solutions consist of an algorithm which finds the optimal assignment in polynomial time, a near-optimal algorithm with less complexity (O(N)), and a distributed algorithm with complexity O(1) that gives acceptable results. To the best of our knowledge, this is the first study presenting an optimal solution for the minimum-energy broadcasting problem for a 2-D network (with cross configuration). We compare our algorithms with the broadcast incremental power (BIP) algorithm, one of the most commonly used methods for solving this problem with complexity O(N²). The results show that while the proposed optimal algorithm finds the best solution, our near-optimal algorithm performs better than BIP in all cases, and the distributed algorithm performs close to it. The performance of our non-optimal algorithms tend to be closer to the optimal solution for larger networks. We prove that all the algorithms perform the same in the asymptotic regime.