Redundant reader is a typical problem which consumes additional power and algorithm overhead for Radio Frequency Identification (RFID) systems development. Therefore, eliminating redundant readers is of great importance to prolong the lifetime of RFID systems. In this paper, we propose a distributed algorithm for redundant reader elimination based on neighboring coverage density (NCD). We also elaborate an optimization scheme leveraging partially movement detection (MD) in RFID systems, called NCDMD. The NCDMD algorithm achieves significant optimization in tag-write operation over NCD. Our experiments show that NCD and NCDMD algorithm are effective and of low overheads as compared to other distributed algorithms. In the performance simulation, we analyze the multi-phase scheme principle and its effect. NCD and NCDMD algorithm can further improve the performance of multi-phase approach in redundant reader elimination.