Towards efficient positional inverted index (Q1662625)

Summary: We address the problem of positional indexing in the natural language domain. The positional inverted index contains the information of the word positions. Thus, it is able to recover the original text file, which implies that it is not necessary to store the original file. Our \textit{Positional Inverted Self-Index} (\texttt{PISI}) stores the word position gaps encoded by variable byte code. Inverted lists of single terms are combined into one inverted list that represents the backbone of the text file since it stores the sequence of the indexed words of the original file. The inverted list is synchronized with a presentation layer that stores separators, \textit{stop words}, as well as variants of the indexed words. The Huffman coding is used to encode the presentation layer. The space complexity of the inverted list is \(\mathcal{O}((N - n) \lceil \log_{2^b} N \rceil +(\lfloor \frac{N - n}{\alpha} \rfloor + n) \times(\lceil \log_{2^b} n \rceil + 1))\) where \(N\) is a number of stems, \(n\) is a number of unique stems, \(\alpha\) is a step/period of the \textit{back pointers} in the inverted list and \(b\) is the size of the word of computer memory given in bits. The space complexity of the presentation layer is \(\mathcal{O}(- \sum_{i = 1}^N \lceil \log_2 p_i^{n(i)} \rceil - \sum_{j = 1}^{N'} \lceil \log_2 p_j' \rceil + N)\) with respect to \(p_i^{n(i)}\) as a probability of a stem variant at position \(i\), \(p_j^\prime\) as the probability of separator or stop word at position \(j\) and \(N^\prime\) as the number of separators and stop words.