## 4 Experiments  
We designed our experiments with respect to the two main questions we asked. What is the performance of PISI compared to the word-based self-indexes proposed by [PERSON] et al. in in [PERSON] et al. (2017)? What is the difference in the search speed of PISI compared to standard positional inverted index? Thanks to the space limits we focus especially on the first question in this paper. To the second question, we can briefly mention that PISI pays for breaking of locality of the stored inverted lists. Depending on the cache size of the computer, PISI can be up to five times slower in searching than the standard positional inverted index. We carried out our tests on Intel(r) CoreTM i7-4702 MQ 2.20 GHz, 8 GB RAM. We used compiler gcc version 4.9.3 with compiler optimization -O3. All reported times represent measured user time + sys time. All our experiments run entirely in RAM. All the reported experiments were performed on bible.txt file of the Canterbury corpus. The first experiment provides a space breakdown of PISI into the single components of the index data structure. Different instances of PISI are stated in the single columns of Table 1 according to setting of the parameters \(\alpha\) (the period of the back pointers) and \(\beta\) (the period of the pointers synchronizing inverted list with the presentation layer). Higher values of both parameters mean better compression ratio but slower decompression. The growing parameter \(\alpha\) reduces the number of the back pointers as well as the reserved bytes. The omitted back pointers cause shorter gaps and thus shorter encoding of the gaps. The parameter \(\beta\) influences only the array \(FP\) which stores the pointers to the presentation layer. Table 1 shows also the space difference between the memory consumption (upper part of the table) and disk storage consumption (lower part of the table). It can be seen that the serialization influences only the vocabulary (.voc file). In the serialized form, the stem variants are encoded only as the suffix extending the stem and the Huffman trees are encoded as simple bit vectors. We demonstrate the effect of the parameters \(\alpha\) and \(\beta\) on the compression ratio and the snippet time in Figure 4. Generally, we can observe that the parameter \(\beta\) has lower impact on the compression ratio and the snippet time than the parameter \(\alpha\). Only the size of \(FP\) array is influenced by \(\beta\) and it is not crucial in terms of the total size of PISI data structure. On the other hand, \(\beta\) impacts the search and decompression process only at one point when the presentation layer \(F\) has to be synchronized with the inverted list \(I\). Thus, lower values of \(\beta\) (i.e., shorter distances between the two following synchronization points) provide only limited gain in terms of the snippet time. Figure 4 proves that the parameter \(\alpha\) significantly impacts the snippet time at the expense of small increase of the necessary  
Figure 3: PISI data structure: the integration with the standard (document-level) inverted index. space. This pays approximately up to the value \(\alpha=20\) when PISI encounters its speed limits. Further increment of \(\alpha\) brings only negligible improvements of the snippet time together with a significant increase of the compression ratio.