Detection of DNA at low abundance with respect to the entire sample is an important problem in areas such as epidemiology and field research, as these samples are highly contaminated with non-target DNA. To solve this problem, many methods have been developed to date, but all require additional time-consuming and costly procedures. Meanwhile, the MinION sequencer developed by Oxford Nanopore Technology (ONT) is considered a powerful tool for tackling this problem, as it allows selective sequencing of target DNA. The main technology employed involves rejection of an undesirable read from a specific pore by inverting the voltage of that pore, which is referred to as Read Until. Despite its usefulness, several issues remain to be solved in real situations. First, limited computational resources are available in field research and epidemiological applications. In addition, a high-speed online classification algorithm is required to make a prompt decision. Lastly, the lack of a theoretical approach for modeling of selective sequencing makes it difficult to analyze and justify a given algorithm.