Single-Sink Multicommodity Flow with Side Constraints

In recent years, several new models for network flows have been analyzed, inspired by emerging telecommunication technologies. These include models of resilient flow, motivated by the introduction of high capacity optical links, coloured flow, motivated by Wavelength-Division-Multiplexed optical networks, unsplittable flow motivated by SONET networks, and confluent flow motivated by next-hop routing in internet protocol (IP) networks. In each model, the introduction of new side-constraints means that a max-flow min-cut theorem does not necessarily hold, even in the setting where all demands are destined to a common node (sink) in the network. In such cases, one may seek bounds on the “flow-cut gap” for the model. Such approximate max-flow min-cut theorems are a useful measure for bounding the impact of new technology on congestion in networks whose traffic flows obey these side constraints.