Distributed Optimization for Combinatorial Coding Subgraph Selection Problems

Many network design cases with network coding can be formulated as combinatorial optimization problems, which are NP-hard and hard to approximate even in a centralized manner. In this paper, guided by Markov approximation framework, we provide a unified distributed solution for one important sub-category of combinatorial network coding problems: combinatorial coding subgraph selection problems. We show the scheme by studying one problem instance: optimal coding subgraph selection over wireline networks under arbitrary bounds on graph diameter . We develop a distributed Markov chain based solution. We obtain analytical results for the impacts of measurement errors on the designed Markov chain. We also discuss the trade-off between the approximation gap and the mixing time of the designed Markov chain. We emphasis that though the analysis is quite involved, the resulting distributed solution is actually simple to implement.