Polynomial time algorithms for multicast network code construction

The famous max-flow min-cut theorem states that a source node s can send information through a network (V, E) to a sink node t at a rate determined by the min-cut separating s and t. 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

Measurements, Models, Systems and Design

531 s.

An effective genetic algorithm for network coding

The network coding problem (NCP), which aims to minimize network coding resources such as nodes and links, is a relatively new application of genetic algorithms (GAs) and hence little work has so far been reported in this area. Most of the existing literature on NCP has concentrated primarily on the static network coding problem (SNCP). There is a common assumption in work to date that a target rate is always achievable at every sink as long as coding is allowed at all nodes. In most real-world networks, such as wireless networks, any link could be disconnected at any time. This implies that every time a change occurs in the network topology, a new target rate must be determined. The SNCP software implementation then has to be re-run to try to optimize the coding based on the new target rate. In contrast, the GA proposed in this paper is designed with the dynamic network coding problem (DNCP) as the major concern. To this end, a more general formulation of the NCP is described. The new NCP model considers not only the minimization of network coding resources but also the maximization of the rate actually achieved at sinks. This is particularly important to the DNCP, where the target rate may become unachievable due to network topology changes. Based on the new NCP model, an effective GA is designed by integrating selected new problem-specific heuristic rules into the evolutionary process in order to better diversify chromosomes. In dynamic environments, the new GA does not need to recalculate target rate and also exhibits some degree of robustness against network topology changes. Comparative experiments on both SNCP and DNCP illustrate the effectiveness of our new model and algorithm