Topology control is a technique used in distributed computing to alter the underlying network (modeled as a graph) to reduce the cost of distributed algorithms if run over the resulting graphs. It is a basic technique in distributed algorithms. For instance, a (minimum) spanning tree is used as a backbone to reduce the cost of broadcast from O(m) to O(n), where m and n are the number of edges and vertices in the graph, respectively. The term "topology control" is used mostly by the wireless ad hoc and sensor networks research community. The main aim of topology control in this domain is to save energy, reduce interference between nodes and extend lifetime of the network. However, recently the term has also been gaining traction with regards to control of the network structure of electric power systems. Topology construction and maintenance Lately, topology control algorithms have been divided into two subproblems: topology construction, in charge of the initial reduction, and topology maintenance, in charge of the maintenance of the reduced topology so that characteristics like connectivity and coverage are preserved. This is the first stage of a topology control protocol. Once the initial topology is deployed, specially when the location of the nodes is random, the administrator has no control over the design of the network; for example, some areas may be very dense, showing a high number of redundant nodes, which will increase the number of message collisions and will provide several copies of the same information from similarly located nodes. However, the administrator has control over some parameters of the network: transmission power of the nodes, state of the nodes (active or sleeping), role of the nodes (Clusterhead, gateway, regular), etc. By modifying these parameters, the topology of the network can change. Upon the same time a topology is reduced and the network starts serving its purpose, the selected nodes start spending energy: Reduced topology starts losing its "optimality as soon as full network activity evolves. After some time being active, some nodes will start to run out of energy. Especially in wireless sensor networks with multihopping, intensive packet forwarding causes nodes that are closer to the sink to spend higher amounts of energy than nodes that are farther away. Topology control has to be executed periodically in order to preserve the desired properties such as connectivity, coverage, density. Topology construction algorithms There are many ways to perform topology