A Deterministic Polynomial-Time Algorithm for Constructing a Multicast Coding Scheme for Linear Deterministic Relay Networks

We propose a new way to construct a multicast coding scheme for linear deterministic relay networks. Our construction can be regarded as a generalization of the well-known multicast network coding scheme of Jaggi

to linear deterministic relay networks and is based on the notion of flow for a unicast session that was introduced by the authors in earlier work. We present randomized and deterministic polynomial-time versions of our algorithm and show that for a network with
$g$
destinations, our deterministic algorithm can achieve the capacity in
$\left \lceil \log (g+1)\right \rceil $
uses of the network and has the fastest construction time among algorithms for this problem.