In this paper, we aim to find a robust network formation strategy that can adaptively evolve the network topology against network dynamics in a distributed manner. We consider a network coding deployed wireless ad hoc network where source nodes are connected to terminal nodes with the help of intermediate nodes. We show that mixing operations in network coding can induce packet anonymity that allows the inter-connections in a network to be decoupled. This enables each intermediate node to consider complex network inter-connections as a node-environment interaction such that the Markov decision process (MDP) can be employed at each intermediate node. The optimal policy that can be obtained by solving the MDP provides each node with optimal amount of changes in transmission range given network dynamics (e.g., the number of nodes in the range and channel condition). Hence, the network can be adaptively and optimally evolved by responding to the network dynamics. The proposed strategy is used to maximize long-term utility, which is achieved by considering both current network conditions and future network dynamics. We define the utility of an action to include network throughput gain and the cost of transmission power. We show that the resulting network of the proposed strategy eventually converges to stationary networks, which maintain the states of the nodes. Moreover, we propose to determine initial transmission ranges and initial network topology that can expedite the convergence of the proposed algorithm. Our simulation results confirm that the proposed strategy builds a network which adaptively changes its topology in the presence of network dynamics. Moreover, the proposed strategy outperforms existing strategies in terms of system goodput and successful connectivity ratio.
Another advantage of network coding is that there is a lower complexity requirement for network formation compared to a conventional store-and-forward approach. In a conventional store-and-forward approach, it is difficult to find the optimal routing path that can achieve the capacity upper bound. Even though an optimal routing solution exists in some cases, such as the Steiner tree in multicast routing, finding the solution is still very complex within a centralized setting @cite_49 . Network coding, however, can transform complex network formation problems into low-complexity distributed problems. For example, a distributed solution that satisfies optimality condition to minimum delay and minimum energy consumption is proposed in @cite_51 . Decentralized algorithms for network formation that can minimize cost per unit capacity are proposed in @cite_5 .
@cite_5 @cite_51 @cite_49
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The following network computing problem is considered. Source nodes in a directed acyclic network generate independent messages and a single receiver node computes a target function f of the messages. The objective is to maximize the average number of times f can be computed per network usage, i.e., the “computing capacity”. The network coding problem for a single-receiver network is a special case of the network computing problem in which all of the source messages must be reproduced at the receiver. For network coding with a single receiver, routing is known to achieve the capacity by achieving the network min-cut upper bound. We extend the definition of min-cut to the network computing problem and show that the min-cut is still an upper bound on the maximum achievable rate and is tight for computing (using coding) any target function in multi-edge tree networks. It is also tight for computing linear target functions in any network. We also study the bound's tightness for different classes of target functions. In particular, we give a lower bound on the computing capacity in terms of the Steiner tree packing number and a different bound for symmetric functions. We also show that for certain networks and target functions, the computing capacity can be less than an arbitrarily small fraction of the min-cut bound. The throughput of wireless networks can be significantly improved by multi-channel communications compared with single-channel communications since the use of multiple channels can reduce interference influence. In this paper, we study interference-aware topology control and QoS routing in IEEE 802.11-based multi-channel wireless mesh networks with dynamic traffic. Channel assignment and routing are two basic issues in such networks. Different channel assignments can lead to different network topologies. We present a novel definition of co-channel interference. Based on this concept, we formally define and present an effective heuristic for the minimum INterference Survivable Topology Control (INSTC) problem which seeks a channel assignment for the given network such that the induced network topology is interference-minimum among all K-connected topologies. We then formulate the Bandwidth-Aware Routing (BAR) problem for a given network topology, which seeks routes for QoS connection requests with bandwidth requirements. We present a polynomial time optimal algorithm to solve the BAR problem under the assumption that traffic demands are splittable. For the non-splittable case, we present a maximum bottleneck capacity path routing heuristic. Simulation results show that compared with the simple common channel assignment and shortest path routing approach, our scheme improves the system performance by 57 on average in terms of connection blocking ratio. Compared to single-hop networks such as WiFi, multihop infrastructure wireless mesh networks (WMNs) can potentially embrace the broadcast benefits of a wireless medium in a more flexible manner. Rather than being point-to-point, links in the WMNs may originate from a single node and reach more than one other node. Nodes located farther than a one-hop distance and overhearing such transmissions may opportunistically help relay packets for previous hops. This phenomenon is called opportunistic overhearing listening. With multiple radios, a node can also improve its capacity by transmitting over multiple radios simultaneously using orthogonal channels. Capitalizing on these potential advantages requires effective routing and efficient mapping of channels to radios (channel assignment (CA)). While efficient channel assignment can greatly reduce interference from nearby transmitters, effective routing can potentially relieve congestion on paths to the infrastructure. Routing, however, requires that only packets pertaining to a particular connection be routed on a predetermined route. Random network coding (RNC) breaks this constraint by allowing nodes to randomly mix packets overheard so far before forwarding. A relay node thus only needs to know how many packets, and not which packets, it should send. We mathematically formulate the joint problem of random network coding, channel assignment, and broadcast link scheduling, taking into account opportunistic overhearing, the interference constraints, the coding constraints, the number of orthogonal channels, the number of radios per node, and fairness among unicast connections. Based on this formulation, we develop a suboptimal, auction-based solution for overall network throughput optimization. Performance evaluation results show that our algorithm can effectively exploit multiple radios and channels and can cope with fairness issues arising from auctions. Our algorithm also shows promising gains over traditional routing solutions in which various channel assignment strategies are used. One central issue in practically deploying network coding is the adaptive and economic allocation of network resource. We cast this as an optimization, where the net-utility-the difference between a utility derived from the attainable multicast throughput and the total cost of resource provisioning-is maximized. By employing the MAX of flows characterization of the admissible rate region for multicasting, this paper gives a novel reformulation of the optimization problem, which has a separable structure. The Lagrangian relaxation method is applied to decompose the problem into subproblems involving one destination each. Our specific formulation of the primal problem results in two key properties. First, the resulting subproblem after decomposition amounts to the problem of finding a shortest path from the source to each destination. Second, assuming the net-utility function is strictly concave, our proposed method enables a near-optimal primal variable to be uniquely recovered from a near-optimal dual variable. A numerical robustness analysis of the primal recovery method is also conducted. For ill-conditioned problems that arise, for instance, when the cost functions are linear, we propose to use the proximal method, which solves a sequence of well-conditioned problems obtained from the original problem by adding quadratic regularization terms. Furthermore, the simulation results confirm the numerical robustness of the proposed algorithms. Finally, the proximal method and the dual subgradient method can be naturally extended to provide an effective solution for applications with multiple multicast sessions