Japanese knotweed is a virulently invasive plant, as are bamboo, garlic mustard and kudzu, just to name a few examples. Eraticating them is a herculean task.
Mt family maintains a small pocket park in Arlington, Ma., off the bike path and used as a rest stop for bikers. The landscapers come through every month during the growing season and weedwhack the knotweed to the ground. it grows back almost over night. The roots run horizontally below the soil line, similar to mint.