New heuristics for strong minimum energy topology with reduced time complexity

The strong minimum energy topology (SMET) problem is to assign transmission range to a set of sensors, such that the resulting topology is strongly connected and the sum of transmit powers of all the sensors is minimized. This problem, having wide range of applications, is known to be NP-hard and also APX-hard for 3-dimension space. Several heuristics and approximation algorithms have been proposed for this problem. In this paper, we first present an enhanced version of Prim-incremental power greedy heuristic which improves the running time of the existing algorithm by a factor of n, i.e., from O(n
³
) to O(n
²
), where n is the number of nodes in the network. Simulations results are also presented to support the theoretical result. Next we propose a new heuristics for SMET problem called Hybrid heuristic, which is based on BorÛvka and Prim MST algorithms and is shown to have lower complexity than both of them. Lastly, we show that this Hybrid heuristics which can provide energy efficiency gains over the existing ones is also the fastest power greedy heuristics for SMET problem when the nodes and links of the network form a planar graph.