We consider the problem of survivable minimum power bidirectional topology optimization in wireless networks with sectored antennas. In this paper, we take an algebraic view of graph connectivity, which is defined as the second smallest eigenvalue of the laplacian matrix of a graph. We propose a (sub-optimal) centralized heuristic procedure for constructing power efficient $K$-node connected topologies. The procedure comprises a construction phase and an improvement phase. The construction phase is based on Kruskal's algorithm for the minimum spanning tree (MST) problem. However, unlike Kruskal's MST algorithm which chooses minimum cost edges from a set of edge weights, our algorithm uses an incremental cost mechanism to select edges. This incremental cost mechanism is motivated by the inherently broadcast nature of the wireless medium. The topology improvement phase is used to remove non-essential edges from the construction phase, without affecting the desired connectivity. |