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There are two challenges for the frame-slotted ALOHA algorithms in radio-frequency identification (RFID). The first challenge is estimating unknown tag-set size accurately; the second challenge is improving the efficiency of the arbitration process so that it uses less time slots to read all tags. This study proposes estimation algorithm based on the Poisson distribution theory and identifies the overestimation phenomenon in full collision. Our novel anticollision algorithm alternates two distinct reading cycles for dividing and solving tags in collision groups. This makes it more efficient for a reader to identify all tags within a small number of time slots.