The 31 European tourists in seven groups who disappeared in southern Algeria trying to cross the Sahara Desert from February through April have all been abducted and are alive, according to government officials. The travelers are evidently being held in a camp in the region of Illizi, near the Libyan border. Their abductors have been variously described as smugglers, Islamic insurgents and terrorists. Travel through these sparsely populated regions is difficult and dangerous because of such political risks and the harsh conditions of the desert.