Good discussion!!!
Every department is different and searching with or without a line real depends on your man power, training, experience, and conditions at each fire. That being said the fastest and most efficient way is to divide and conquer by separating the search and attack teams. I think silverfish is right in emphasizing that these functions should be in conjunction with each other. Searching with a hose line is like using a tool designed to do 10 different things. It may do multiple things but it does none of them well.