## 1 Introduction  
The sequence tag concept was introduced by [PERSON] in 1994 [1]. It refers to the partial sequence of amino acids derived from a series of continuous fragment ions. Sequence tag searching combines the advantages of database search [2] and de novo sequencing [3] in mass spectrometry analysis. In protein identification, protein databases are frequently searched but updated infrequently. The construction of an index can significantly enhance retrieval speed [4]. The sequence tag index, abbreviated as tag index, is an indexing technique that reduces the search time complexity by establishing a mapping between sequence tags and corresponding sites in the protein database. In recent years, the tag index, as an important acceleration technique, has been adopted by many modern protein search engines. The FM-index is an index scheme based on the Burrows-Wheeler transform [5]. To facilitate the implementation of the string matching algorithm, TagGraph uses the FM-index to construct an index for protein databases [6], and the index is referred to as the FM-indexed Protein. TagGraph performs sequence-splitting searches on de novo sequencing results obtained from PEAKS [7]. Then, it uses the FM-indexed Protein to search for sequence tags in the protein database. In 2024, PIPI2 continued to use this method, and it constructed tag indexes based on the FM-index to achieve the rapid retrieval of protein databases [8]. A tag index based on an inverted index is essentially a hash table where the substrings in protein sequences serve as keys and values contain information such as the position of the substring in the original protein sequence. The inverted index solves the memory expansion issue that occurs during the construction of an FM-index, making it more practical for applications. In a tag index, each sequence tag corresponds to an inverted list that consists of protein IDs and the starting positions of the sequence tag within the protein. Compared to traditional pattern-matching algorithms, this method significantly improves efficiency and optimizing time complexity from \(O(N*M)\) to \(O(1)\), where \(N\) represents the length of the protein sequence and \(M\) represents the length of the sequence tag. To enhance the efficiency of protein identification, an ion index design scheme based on an inverted index was proposed [9], which accelerates the protein search by constructing an ion mass index. In 2010, a protein sequence database organization algorithm based on the longest common prefix (ABLCP) was proposed [10]. This method eliminates redundant candidate peptide segments in the database, reducing the number of peptide spectrum matches. Many protein search engines have continued to use inverted indexes to construct ion mass indexes, such as Interrogator [11], pFind-alioth [12], and MSFragger [13]. In order to meet the demand for the rapid retrieval of sequence tags in protein sequence databases, Open-pFind [14] designs a tag index architecture using an inverted index model. Sequence tags are stored in the inverted index in a lexicographic order. The correspondence between tags and hash values is as follows:  
\[\text{hash}(T)=\sum_{i=1}^{\text{len}(T)}\left(\text{asc}(a_{i})-\text{asc}( ^{\prime}\text{A}^{\prime})\right)\times 26^{\text{len}(T)} \tag{1}\]  
where \(T\) represents a sequence tag, \(a_{i}\) represents the i-th amino acid in the tag, \(\text{asc}(\cdot)\) is the function for calculating ASCII, and \(\text{len}(\cdot)\) is the function that calculates the length of each tag. In order to reduce space consumption during the protein identification process, MODplus [15] improves on MODa [16] by using a global site encoding strategy to construct tag indexes, concatenating protein sequences for storage, and reducing the index space by 25.79% to 38.79% on the original structure through a single site mapping. In 2022, the tag index TIIP was proposed, which supports the rapid recall of candidate peptides [17].