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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We present decentralized algorithms that compute minimum-cost subgraphs for establishing multicast connections in networks that use coding. These algorithms, coupled with existing decentralized schemes for constructing network codes, constitute a fully decentralized approach for achieving minimum-cost multicast. Our approach is in sharp contrast to the prevailing approach based on approximation algorithms for the directed Steiner tree problem, which is suboptimal and generally assumes centralized computation with full network knowledge. We also give extensions beyond the basic problem of fixed-rate multicast in networks with directed point-to-point links, and consider the case of elastic rate demand as well as the problem of minimum-energy multicast in wireless networks. Optimal data routing in a network can be often understood as a multicommodity flow problem. Given a network and a set of commodities, i.e., a set of source-destination pairs, one tries to achieve certain optimization goal, such as minimum delay, maximum throughput, while maintaining certain fairness among all commodities. The constraints of such optimization problems are usually network link capacity and traffic demand of each commodity. Multicommodity flow problem has been well studied as a typical linear programming problem. Its distributed solutions have also been proposed[2]. The Steiner packing problem is to find the maximum number of edge-disjoint subgraphs of a given graph G that connect a given set of required points S. This problem is motivated by practical applications in VLSI- layout and broadcasting, as well as theoretical reasons. In this paper, we study this problem and present an algorithm with an asymptotic approximation factor of vSv 4. This gives a sufficient condition for the existence of k edge-disjoint Steiner trees in a graph in terms of the edge-connectivity of the graph. We will show that this condition is the best possible if the number of terminals is 3. At the end, we consider the fractional version of this problem, and observe that it can be reduced to the minimum Steiner tree problem via the ellipsoid algorithm.