Presuming from your word choice you refer to my assassination recommendation, vis a vis the King of Cairhien, following major roads or rivers might be a good idea. How did they even find out about the tree being cut down in the first place? Presumably a merchant or someone alowed in the Waste told them. Such people would also be highly likely to know where the city of Cairhien is located.

The idea that they did not know the location of Cairhien city would speak even more poorly of their intelligence for initiating a war against a country about which they had no idea of its general dimensions or the location of the most probable axis of resistance/accumulation of loot! The only thing more stupid than sending a small party of assassins into terra incognita to find a man whom you have no idea where he lives, is sending an army to do the same thing.