In the previous two chapters, we assumed that a coding subgraph specifying the times and locations of packet injections was given. We dealt only with half the problem of establishing connections in coded packet networks — the coding half. This chapter deals with the other half: subgraph selection.

Subgraph selection, which is the problem of determining the coding subgraph to use, is the coded networks analog of the joint problems of routing and scheduling in conventional, routed networks. Subgraph selection and coding are very different problems, and the techniques used in the this chapter differ significantly from those in the previous two chapters. In particular, while the previous two chapters generally used techniques from information theory and coding theory, this chapter generally uses techniques from networking theory.

Subgraph selection is essentially a problem of network resource allocation: we have a limited resource (packet injections) that we wish to allocate to coded packets in such as way as to achieve certain communication objectives. We propose a number of solutions to the problem, and we divide these solutions into two categories: flow–based approaches (Section 5.1) and queue–length–based approaches (Section 5.2). In flow–based approaches, we assume that the communication objective is to establish a set of (unicast or multicast) connections at certain, given flow rates while, in queue–length–based approaches, we suppose that the flow rates, though existent, are not necessarily known, and we select coding subgraphs using the state of packet queues.