On Routing-Optimal Network for Multiple Unicasts

TL;DR

This paper identifies a class of networks called information-distributive networks where routing alone suffices to achieve the same rate region as network coding, based on specific topological features.

Contribution

It introduces the concept of information-distributive networks and characterizes their topological features that make routing optimal for multiple unicast sessions.

Findings

Routing can achieve the entire rate region in certain networks.

Examples include networks from index coding and unicast with deadlines.

Topological features determine routing optimality.

Abstract

In this paper, we consider networks with multiple unicast sessions. Generally, non-linear network coding is needed to achieve the whole rate region of network coding. Yet, there exist networks for which routing is sufficient to achieve the whole rate region, and we refer to them as routing-optimal networks. We identify a class of routing-optimal networks, which we refer to as information-distributive networks, defined by three topological features. Due to these features, for each rate vector achieved by network coding, there is always a routing scheme such that it achieves the same rate vector, and the traffic transmitted through the network is exactly the information transmitted over the cut-sets between the sources and the sinks in the corresponding network coding scheme. We present more examples of information-distributive networks, including some examples from index coding and single unicast with hard deadline constraint.