Minimum-cost multicast over coded packet networks

IEEE Transactions on Information Theory, 2005

The famous max-flow min-cut theorem states that a source node can send information through a network ( ) to a sink node at a rate determined by the min-cut separating and . Recently, it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediate nodes are allowed to re-encode the information they receive. We demonstrate examples of networks where the achievable rates obtained by coding at intermediate nodes are arbitrarily larger than if coding is not allowed. We give deterministic polynomial time algorithms and even faster randomized algorithms for designing linear codes for directed acyclic graphs with edges of unit capacity. We extend these algorithms to integer capacities and to codes that are tolerant to edge failures.

2004

Abstract Optimal data routing in a network can be often understood as a multicommodity flow problem. Given a network and a set of commodities, ie, 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.

IEEE Transactions on Information Theory, 2000

The single-source min-cost multicast problem, which can be framed as a convex optimization problem with the use of network codes and convex increasing edge costs is considered. A decentralized approach to this problem is presented by Lun, Ratnakar et. al. for the case where all users cooperate to reach the global minimum. In this paper, the cost for the scenario where each of the multicast receivers greedily routes its flows is analyzed and the existence of a Nash equilibrium is proved. An allocation rule by which edge cost at each edge is allocated to flows through that edge is presented. It is shown that the flow cost at user equilibrium under the proposed pricing rule is the same as the min-cost. This leads to the construction of a selfish flow-steering algorithm for each receiver, which is also globally optimal. Further, the algorithm is extended for completely distributed flow adaptation at nodes in the network to achieve globally minimal cost in steady state. Analogous results are also presented for the case of multiple multicast sessions.

Journal of Combinatorial Optimization, 2013

Network coding is a technique which can be used to improve the performance of multicast communications by performing encoding operations at intermediate nodes. In real-time multimedia communication applications, there are usually several weights associated with links, such as cost, delay, jitter, loss ratio, security, and so on. In this paper, we consider the problem of finding an optimal multicast sub-graph over coded packet networks, where the longest end-to-end weight from the source to each destination does not exceed an upper bound. First, a mixed integer programming model is proposed to formulate the problem which is NP-hard. Then, a column-generation approach is described for this problem, in which the problem is decomposed into a master linear programming problem and several integer programming sub-problems. Moreover, two methods based on linear and Lagrangian relaxation are proposed to compute a tight lower bound of the optimal solution value. Computational results show that the proposed algorithm provides an efficient way for solving the problem, even for relatively large networks.

IEEE Transactions on Vehicular Technology, 2015

We propose a network coding strategy for multicast applications called the simple network coding scheme, which takes network coding chances raised among adjacent nodes. The proposed scheme incorporates both intrasession and intersession network coding strategies and effectively improves multicast throughput. We characterize the capacity region of the proposed scheme and derive an optimal control algorithm for the proposed scheme. We perform a complexity analysis for the proposed control algorithm and provide some insights into its practical implementation. For a comparison, we also formulate the capacity region of conventional multicast schemes and provide performance evaluation using a linear programming solver. In empirical analyses, we investigate how the proposed scheme improves multicast throughput gains from various perspectives (i.e., the number of flows, the number of network coded packets, and split-multicast) and find out that most of the gains can be achieved by simple pairwise network coding with non-split-multicast. We observe dramatic throughput gains up to 75% beyond the conventional schemes on random topologies with ten nodes.

IEEE Journal on Selected Areas in Communications, 2006

A central issue in practically deploying network coding in a shared network is the adaptive and efficient allocation of network resources. This issue can be formulated as an optimization problem of maximizing the net-utility -the difference between a utility derived from the attainable multicast throughput and the total cost of resource provisioning. We develop a primal-subgradient type distributed algorithm to solve this utility maximization problem. The effectiveness of the algorithm hinges upon two key properties we discovered: (1) the set of subgradients of the multicast capacity is the convex hull of the indicator vectors for the critical cuts, and (2) the complexity of finding such critical cuts can be reduced by exploiting the algebraic properties of linear network coding. The extension to multiple multicast sessions is also carried out. The effectiveness of the proposed algorithm is confirmed by simulations on an Internet Service Provider's topology.

Manufacturing Engineer

This paper proposes deterministic algorithms for decentralized network coding. Decentralized coding allows to locally specify the coding operations at network nodes without knowledge of the overall network topology, and to accommodate future changes in the network such as addition of receivers. To the best of our knowledge, these are the first deterministic decentralized algorithms proposed for network coding.

2006

A fundamental problem faced in the design of almost all packet networks is that of efficient operation-of reliably communicating given messages among nodes at minimum cost in resource usage. We present a solution to the efficient operation problem for coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. Such networks are in contrast to conventional, routed packet networks, where outgoing packets are restricted to being copies of received packets and where reliability is provided by the use of retransmissions. This thesis introduces four considerations to coded packet networks: 1. efficiency, 2. the lack of synchronization in packet networks, 3. the possibility of broadcast links, and 4. packet loss. We take these considerations and give a prescription for operation that is novel and general, yet simple, useful, and extensible. We separate the efficient operation problem into two smaller problems, which we call network coding-the problem of deciding what coding operation each node should perform given the rates at which packets are injected on each link-and subgraph selection-the problem of deciding those rates. Our main contribution for the network coding problem is to give a scheme that achieves the maximum rate of a multicast connection under the given injection rates. As a consequence, the separation of network coding and subgraph selection results in no loss of optimality provided that we are constrained to only coding packets within a single connection. Our main contribution for the subgraph selection problem is to give distributed algorithms that optimally solve the single-connection problem under certain assumptions. Since the scheme we propose for network coding can easily be implemented in a distributed manner, we obtain, by combining the solutions for each of the smaller problems, a distributed approach to the efficient operation problem. Preface Vladimir Nabokov once opined, "My loathings are simple: stupidity, oppression, crime, cruelty, soft music. My pleasures are the most intense known to man: writing and butterfly hunting." I share all of Nabokov's loathings, but only one of his pleasures-and that began only recently. Of course, the lepidoptera I've been involved with are none that Nabokov would recognize or, I imagine, much revere. Nevertheless, the butterflies to which I refer-from the butterfly network of Ahlswede et al. (see Figure 7 of [2]) to its wireless counterpart (see Figure 1 of [73]) to further generalizations-have certainly given me a great deal of pleasure since I began investigating network coding in the spring of 2003. This thesis represents the culmination of my work over the last three years, which began with the simple question, how would all this actually work? I was intrigued by network coding. But I couldn't quite reconcile it with the way that I understood data networks to operate. So I thought to take the basic premise of network coding and put it in a model that, at least to me, was more satisfying. The following pages lay out a view of coded packet networks that, while certainly not the only one possible, is one that I believe is simple, relevant, and extensible-I can only hope that it is sufficiently so to be truly useful.

2012

In today's practical networks, end-to-end information delivery is performed by routing. Network coding generalizes routing by allowing a node to generate output data by mixing (i.e., computing certain functions of) its received data. Network coding techniques are used to find the minimum cost in given network. In wire line network, solving for the optimal coding subgraphs in network coding is equivalent to finding the optimal routing scheme in a multi-commodity flow problem. Multicast is an important factor for the communication in wireless network. This problem is also known as NP-complete. This paper focuses on the solution for the above problem and provides the analytical framework as well as distributed algorithm in multicast session. A set of node based distributed algorithm are designed at sources node and virtual at intermediate node. Keyword-Network coding, multi-commodity flow problem, distributed algorithm, wireless networks.

2006 IEEE International Symposium on Information Theory, 2006

Many of the multimedia applications such as video broadcasting and teleconferencing require the network to support dynamic multicast sessions when the membership of the multicast group changes over time. In this paper, we study this problem in the context of coded networks. While trying to minimize the cost of the multicast, we also want to minimize the disturbances to existing users when the multicast graph changes. To characterize disturbances to users, we define two types of rearrangements, link rearrangements and code rearrangements. We present four algorithms to solve the non-rearrangeable and rearrangeable versions of the dynamic multicast problem. Simulation results show that the α-scaled algorithm we proposed can keep the cost of the multicast close to that of the optimal solution when the multicast subgraph evolves, and, at the same time, causes very few rearrangements during the process.