... to Jungle
The jungle shows all the possible solutions - all those which are not definitely non-optimal - in which we shall find the globally optimal solution(s) for the event costs we have. While this is definitely a complex figure, it is much less complex than listing all the complete solutions, to the problem.
Each arc is coded with a cost determined by the evolutionary events it implie, and the whole figure is traversed from tips to root of the associate tree (reverse direction from the direction of the arcs). At each stage the least cost subjungle is recorded for each feasible set of host switches in the subjungle. This means that if there is a lot of host switching then complexity rises very quickly - but itís unavoidable.