 This pilot phase I and randomized phase II trial studies the best way to perform axillary lymph node preservation surgery and to see how well it works in preventing lymphedema in patients with breast cancer. Lymph node mapping may help in planning surgery to remove breast cancer and affected lymph nodes. It is not yet known whether reverse mapping guided axillary lymph node dissection is more effective than standard axillary lymph node dissection in preventing lymphedema. 