**2. Background**

This section discusses the effects of topology control on the operation of a network, gives the taxonomy of the topology control schemes for multihop wireless networks, and presents some related well-known topology control algorithms. The section also contains a taxonomical classification of the channel assignment schemes for wireless mesh networks, and discusses some related well-known channel assignment algorithms for each class.

### **2.1. Topology control schemes**

The importance of Topology Control (TC) lies in the fact that it affects network spatial reuse and hence the traffic carrying capacity. Choosing a large transmit power results in excessive interference, while choosing a small transmit power results in a disconnected network [5]. Using TC through transmission power control, the network connectivity and hence the network topology is affected, interference levels are mitigated, which reduces the co-channel interference, and the opportunity of spatial channel re-use is enhanced [6].

### *2.1.1. Topology control in multi-radio WMNs*

The connectivity graph in a multi-radio WMN is determined through topology control. So, the problem of TC in multi-radio WMNs involves the selection of transmission power for each radio interface of each mesh node in the network, so as to maintain the network connectivity with the use of minimum power.
