## 2 Related Work  
The multichannel multi-radio approach in IEEE 802.11 based wireless networks has been widely studied by a number of researchers and can be categorized as centralized and distributed approaches. The centralized approach has been further categorized as:  
* Flow based
* Graph based
* Partition based  
A centralized flow based approach presented in [22,23,36,37] proposes a centralized joint channel assignment and multi-path routing algorithm. The channel assignment algorithm first considers high load edges. The routing algorithm uses both shortest path routing and randomized multi-path routing which is a set of paths used between any pair of communicating nodes. The joint channel assignment and multi-path routing algorithm proceeds in an iterative fashion. However, their algorithm is based on heuristics and the worst performance bound on its performance is not known. In addition to their scheme no guarantees on fair allocation of bandwidth is provided. However, a simulation study shows that by deploying just two NICs per node, it is possible to achieve an eight-fold improvement in the overall network goodput, when it is compared with the conventional single-NIC-per-node in wireless _ad hoc_ networks. This is inherently limited to one single radio channel. In [22] they assume that there is no system or hardware support to allow a radio interface to switch channels on a per-packet basis. They also assume a radio interface is capable of switching channels rapidly and is supported by system software. Their evaluation demonstrates that our algorithm can effectively exploit the increased number of channels and radios, and performs much better than the theoretical worst case bounds. [PERSON] _et al._[36] define a standard multi-commodity flow problem on a MC-MR network; they assume that the traffic demand for different source destination pairs is given in the form of a rate vector. In their algorithms, it is not clear if it is possible to jointly optimize routing, link channel assignment and scheduling in a distributed manner. A centralized, graph based approach has been proposed in [38, 39, 40], where links and nodes are considered as edges and vertices of a graph respectively in formulating radio and channel assignment by assigning edges to vertices. The limitation of these methods is that it is very difficult to capture network load information with a graph model. Network flow based centralized approaches can be found in [22, 23] and [36], where multi radio multichannel is modeled based on network flows to overcomes the limitations associated with graph based approaches. These approaches are not realistic as constant traffic sources are assumed all the time while network traffic can be bursty in nature. [PERSON] _et al._[38] have considered the channel assignment, radio-channel mapping problem in multi-radio wireless mesh networks. They have argued that a traffic-independent channel assignment that provides a connected and low interference topology can serve as a basis for dynamic, efficient and flexible utilization of available channels and radios. In [28] a simple approach to address this issue is common channel assignment (CCA) which assumes that radio interfaces at each node are assigned to the same set of channels. This leads to inefficient channel utilization in the typical case where number of interfaces per node is fewer relative to the number of channels. Another graph based approach studied in [40] on an extensive evaluation via simulations shows that multi-radio scenarios, yields performance gains in excess of 40% compared to a static assignment of channels. In [41], the authors have addressed co-existence of heterogeneous interfaces and introduced a radio based novel graph model which captures the heterogeneity of interfaces. A partition approach [42] designs a new algorithm that takes advantage of the inherent multi-radio capability of Wireless Mesh Networks (WMNs).