Minimum-cost multicast over coded packet networks

We consider the problem of establishing minimum-cost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomial-time solvable optimization problem, and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimum-cost multicast. By contrast, establishing minimum-cost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved

Network coding with periodic recomputation for minimum energy multicasting in mobile ad-hoc networks

We consider the problem of minimum-energy multicast using network coding in mobile ad hoc networks (MANETs). The optimal solution can be obtained by solving a linear program every time slot, but it leads to high computational complexity. In this paper, we consider a low-complexity approach, network coding with periodic recomputation, which recomputes an approximate solution at fixed time intervals, and uses this solution during each time interval. As the network topology changes slowly, we derive a theoretical bound on the performance gap between our suboptimal solution and the optimal solution. For complexity analysis, we assume that interior-point method is used to solve a linear program at the first time slot of each interval. Moreover, we can use the suboptimal solution in the preceding interval as a good initial solution of the linear program at each fixed interval. Based on this interior-point method with a warm start strategy, we obtain a bound on complexity. Finally, we consider an example network scenario and minimize the complexity subject to the condition that our solution achieves a given optimality gap

Content Distribution by Multiple Multicast Trees and Intersession Cooperation: Optimal Algorithms and Approximations

In traditional massive content distribution with multiple sessions, the sessions form separate overlay networks and operate independently, where some sessions may suffer from insufficient resources even though other sessions have excessive resources. To cope with this problem, we consider the universal swarming approach, which allows multiple sessions to cooperate with each other. We formulate the problem of finding the optimal resource allocation to maximize the sum of the session utilities and present a subgradient algorithm which converges to the optimal solution in the time-average sense. The solution involves an NP-hard subproblem of finding a minimum-cost Steiner tree. We cope with this difficulty by using a column generation method, which reduces the number of Steiner-tree computations. Furthermore, we allow the use of approximate solutions to the Steiner-tree subproblem. We show that the approximation ratio to the overall problem turns out to be no less than the reciprocal of the approximation ratio to the Steiner-tree subproblem. Simulation results demonstrate that universal swarming improves the performance of resource-poor sessions with negligible impact to resource-rich sessions. The proposed approach and algorithm are expected to be useful for infrastructure-based content distribution networks with long-lasting sessions and relatively stable network environment

Minimum cost mirror sites using network coding: Replication vs. coding at the source nodes

Content distribution over networks is often achieved by using mirror sites that hold copies of files or portions thereof to avoid congestion and delay issues arising from excessive demands to a single location. Accordingly, there are distributed storage solutions that divide the file into pieces and place copies of the pieces (replication) or coded versions of the pieces (coding) at multiple source nodes. We consider a network which uses network coding for multicasting the file. There is a set of source nodes that contains either subsets or coded versions of the pieces of the file. The cost of a given storage solution is defined as the sum of the storage cost and the cost of the flows required to support the multicast. Our interest is in finding the storage capacities and flows at minimum combined cost. We formulate the corresponding optimization problems by using the theory of information measures. In particular, we show that when there are two source nodes, there is no loss in considering subset sources. For three source nodes, we derive a tight upper bound on the cost gap between the coded and uncoded cases. We also present algorithms for determining the content of the source nodes.Comment: IEEE Trans. on Information Theory (to appear), 201