Answer: Yes (but backyard composters beware!)
It’s ok to put non-native invasive plants (including trimmings, roots and leaves) in your food and yard waste cart.
However, backyard compost is a different story. Don’t put weed seed heads, roots, or runners in your backyard compost heap—they’ll just continue to grow! Instead, dry them out in the sun or let them rot inside a black plastic bag until they’re dead (then compost them) or put them in your food and yard waste cart.