To defeat weeds, show no mercy

At Kitchen Gardeners International and The Washington Post, Barbara Damrosch writes about weeds.

My own personal weed challenge comes in the form of dollarweed, also called pennywort. (If you're not familiar with what it looks like, here's a photo and description.) Since it spreads by runners, it's virtually impossible to eradicate; it regrows from any pieces left in the soil. I've weeded it, and weeded it, and weeded it again in an ongoing battle that has lasted close to two years now. My next try is going to be to solarize one of my beds that's out of cultivation at the moment.

Anyone have other suggestions?