Complexity of Source-Sink Monotone 2-parameter min cut

There are many applications of max flow with capacities that depend on one or more parameters. Many these fall into the “Source-Sink Monotone” framework, a special case Topkis's monotonic optimization which implies parametric min cuts nested. When there is single parameter, this property number distinct linear in nodes, quite useful for constructing algorithms to identify all possible cuts. multiple Source-Sink Monotone parameters, and vectors parameters ordered usual vector sense, resulting still However, was an open question. We show even only two can be exponential nodes.