Sublinear-Time Non-Adaptive Group Testing With <i>O</i>(<i>k</i> log <i>n</i>) Tests via Bit-Mixing Coding

The group testing problem consists of determining a small set defective items from larger based on tests groups items, and is relevant in applications such as medical testing, communication protocols, pattern matching, many more. While rigorous algorithms have long been known with runtime at least linear the number recent line works has sought to reduce poly(k log n), where n k defectives. In this paper, we present an algorithm for non-adaptive termed bit mixing coding (BMC), which builds techniques that encode item indices test matrix, while incorporating novel ideas erasure-correction coding. We show BMC achieves asymptotically vanishing error probability O(k n) 2 · runtime, limit ? ? (with having arbitrary dependence n). This closes open simultaneously achieving decoding time using without any assumptions k. addition, same scaling laws can be attained commonly-considered noisy setting, each outcome flipped constant probability.