Do TSA body searches violate 4th amendment?

Today's question in the ongoing saga of TSA's body scanners and the alternative full-body patdown and / or groping: Do the techniques you must submit to in order to fly amount to "unreasonable" searches, as courts would define the 4th amendment to the U.S. Constitution? That's among the questions raised in this New York Times story, which otherwise repeats much of what's been written and said for the last several weeks, in this space and elsewhere, about the new way of doing airport security.