Abstract: A major challenge in wireless underground sensor networks is the signal attenuation originated from multi-environment transmission between underground sensor nodes and the above-ground base station. To overcome this issue, an efficient approach is deploying a set of relay nodes aboveground, thereby reducing transmission loss by shortening transmitting distance. However, this introduces several new challenges, including load balancing and transmission loss minimization. This paper tackles the problem of deploying relay nodes to reduce transmission loss under a load balancing constraint by proposing two approximation algorithms. The first algorithm is inspired by Beam Search, combined with a new selection scheme based on Boltzmann distribution. The second algorithm aims to further improve the solutions obtained by the former by reducing the transmission loss. We observe that we can find an optimal assignment between sensor nodes and a set of the chosen relay in polynomial time by reformulating the part of the problem as a bipartite matching problem with minimum cost. Experimental results indicate that the proposed methods perform better than the other existing ones in most of our test instances while reducing the execution time.
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