Revisiting RFID Missing Tag Identification: Theoretical Foundation and Algorithm Design

We revisit the problem of missing tag identification in RFID networks by making three contributions. Firstly, we quantitatively compare and gauge the existing propositions spanning over a decade on missing tag identification. We show that the expected execution time of the best solution in the literature is $\Theta \left ({{N+\frac {(1-\alpha )^{2}(1-\delta )^{2}}{ \epsilon ^{2}}}}\right )$ , where $\delta $ and $\epsilon $ are parameters quantifying the required identification accuracy, N denotes the number of tags in the system, among which $\alpha N$ tags are missing. Secondly, we analytically establish the expected execution time lower-bound for any missing tag identification algorithm as $\Theta \left ({{\frac {N}{\log N}+\frac {(1-\delta )^{2}(1-\alpha )^{2}}{\epsilon ^{2} \log \frac {(1-\delta )(1-\alpha )}{\epsilon }}}}\right )$ , thus setting the theoretical performance limit. Thirdly, we develop two novel missing tag identification algorithms with the expected execution time of $\Theta \left ({{\frac {\log \log N}{\log N}N+\frac {(1-\alpha )^{2}(1-\delta )^{2}}{ \epsilon ^{2}}}}\right )$ , reducing the time overhead by a factor of up to $\log N$ over the best algorithm in the literature. The key technicality in our first algorithm is a novel data structure termed as collision-partition tree (CPT), built on a subset of bits in tag pseudo-IDs, leading to a more balanced tree structure and reducing the time complexity in parsing the entire tree. To further improve time efficiency, our second algorithm integrates multiple CPTs to form a collision-partition forest (CPF), reducing both the number of slots and the quantity of information broadcasting.