There seems to be confusion in this thread between "invasive" (aggressive proliferation causing significant displacement or harm to native populations of plants and/or animals) and "aggressive" (rapidly spreading growth in a localized area). Just because you don't see a plant colonizing the area near where you planted a specimen, doesn't in any way mean it's not invasive and causing problems. Also, just because you do, doesn't mean it is invasive. One reasonable way to make a decision about whether, in regards to potential for invasiveness, a plant should be planted in a particular area (state, part of the country, etc) is to review reports from appropriate state agencies or organizations like Exotic Pest Plant Councils. If a plant is reported to be an invasive problem in your area, then planting it is probably not an an environmentally responsible thing to do. If, on the other hand, there is no issue anywhere around your (in your part of the country), then plant away and enjoy.

Getting rid of Japanese knotweed [aka Japanese Bamboo] is do-able; doing so requires persistence. I got rid of a patch somewhat bigger than yours by digging out the plants as best I could and then by assiduously cutting back new growth as soon as it appeared. [This starves the plant for light and interrupts photosynthesis.] After the initial digging out of individual plants, the maintenanceÂclipping new growthÂwas pretty easy. Even mowing works; it just takes near-daily diligence. The patch never recovered and within two years was 100% knotweed-free, and has remained so for the past 15 years. Herbicides work, too, but they will kill the juniper as well and will not completely kill the knotweed's underground root system, so you're still left with clipping. If you do choose the chemical route, spray the knotweed when it is in flower (late summer). But try the non-chemical method; it repays efforts with a lot of personal gratification.

I have seen very well behaved varieties and of course there are the incredibly invasive varieties. These pictures look a lot like the variety I had. I planted 4 of these from 3" pots about 3 years ago. I needed to remove them this year for an irrigation system. After 4 weeks of repeated applications of glyphosate, I ended up having to dig them out of the ground. The roots were 2-3 feet deep. It's an incredibly tough plant. More like a very hardy shrub that grows anew each year than a typical perrenial. It was a pretty plant when they were young then they were a huge nuissance. I was constantly pruning to keep them under control. I would not recommend them unless you want them to take over a fairly large portion of your yard. Aaron Here is a link that might be useful:

Tilling wont spread this pest, it will probably help you a little though. Its not the seeds that you have to worry about, its the roots. This bad boy can sprout from as small a piece of root as 1 inch, and can live underground covered up by plastic for up to 5 years. The knot weed will just come up arround the plastic. However, It doesnt like lime,it doesnt like to be mown, and it has a hard time comming up through a healthy bed of grass... ( it will try though, if it has no other option). My recomendation would be to till up your piece of ground, and remove as many of the roots as you possibly can. Then mix large qty's of lime into the soil, and cover with heavy plastic, and build your raised beds. Lime the "infected area" arround your beds, add grass seed, and weed out any emerging shoots with extreem predjiduce! When your grass starts growing, mow it religiously! Ive successfully gotten rid of it from my yard using this method.