Should Cities Ban Invasive Plants?

We're doing something a bit different for this week's Friday forum: a debate question.  It's inspired by my mother, who just bought a house next to a fellow who loves to grow bamboo.  It's about 10-12 feet high, maybe more, shading her windows and dropping leaves into her yard.  More problematically, it seems to be sending roots over to her yard.  Unfortunately, she didn't know when she bought the house that bamboo is a highly invasive plant that can wreak havoc with things like sidewalks and foundations.  Yeah, I know; this is what comes of living in Manhattan for forty years.

DC, alas, does not have an ordinance against such plants, though local laws against bamboo are apparently rising in popularity.  

But should it?  If you libertarians wonder why I say that not all questions can be solved by resort to first principles and property rights, this is why.  The plants are on his property, but they're invading hers.  On the other hand, there are limits to one's ability that the neighbors alter their landscape to suit your preferences: my neighbor has a bumper crop of dandelions going every spring, but I don't think that either an ordinance or a lawsuit are in order.  I weed and occasionally resort to Roundup, and don't feel too hard-used.  In return, he doesn't complain about the debris shed from . . . well, whatever the hell kind of tree it is that we have out back.  (Yeah, I know.  Like I said: decades in Manhattan.)

So I'll throw it out to my audience, libertarian-leaning and otherwise.  Should governments ban invasive plants that can wreak havoc with neighboring property, or at least require the owners to keep them under control?  And if so, how should such rules be framed so that you don't have neighbors suing each other over crabgrass?