Abstract: We consider the extrema estimation problem in large-scale radio-frequency identification (RFID) systems, where there are thousands of tags and each tag contains a finite value. The objective is to design an extrema estimation protocol with the minimum execution time. Because the standard binary search protocol wastes much time due to interframe overhead, we propose a parameterized protocol and treat the number of slots in a frame as an unknown parameter. We formulate the problem and show how to find the best parameter to minimize the worst-case execution time. Finally, we propose two rules to further reduce the execution time. The first is to find and remove redundant frames. The second is to concatenate a frame from minimum value estimation with a frame from maximum value estimation to reduce the total number of frames. Simulations show that, in a typical scenario, the proposed protocol reduces execution time by 79% compared with the standard binary search protocol.