Since I've lived here, every Spring some kind of plant grows right up against the side of the house.
This plant can grow at least 6 inches overnight once things start warming up.
It spreads (over & underground) as it grows & unless I trim it back periodically, I'm sure that it would take over the entire walkway between the house & the garage!
We never knew what it was so just called it "alien bamboo" since when it matures, the huge stalks are exactly like bamboo and it grows so fast you'd think it came from another planet!
I was in a waiting room the other day leafing through an old Readers Digest and lo and behold! There it was! - a picture of the plant, a name for it and description etc.
Here's what it said;

"Like many invasive alien plants, this Asian native of the buckwheat family was introduced to North America in the late 19th century as an ornamental. It is now found throughout much of Canada. Growing one to three metres (3-10ft)high it forms large, dense stands along open areas such as lakes, rivers and roadways, completely crowding out native vegetation. The deep root system can push the near-unstoppable shoots through pavement, foundations and concrete drains, resulting in expensive damege. The International Union for Conservation of Nature pegs it as one of the world's 100 worst invasive species. (Oh great!@) If a small patch is found, mature plants can be dug up, or young shoots can be pulled out of the ground. Larger infestations require the use of chemicals by experts."

Did you note the words in the description of "alien" and "Asian?" - we weren't too far wrong in our name for it!

So, providing I prune the branches and catch the underground shoots as they appear in the walkway, it makes for a lovely green leafy "canopy" between the house and the garage during the hot summers.
In late summer, it throws beautiful white flowers (somewhat like lilac blossoms) which attract loads of bees and butterflies.
So as long as it's manageable and behaves itself, it can stay.