Some theoretical and experimental observations on permutation spaces and similarity search

Permutation based approaches represent data objects as ordered lists of predefined reference objects. Similarity queries are executed by searching for data objects whose permutation representation is similar to the query one. Various permutation-based indexes have been recently proposed. They typically allow high efficiency with acceptable effectiveness. Moreover, various parameters can be set in order to find an optimal trade-off between quality of results and costs. In this paper we studied the permutation space without referring to any particular index structure focusing on both theoretical and experimental aspects. We used both synthetic and real-word datasets for our experiments. The results of this work are relevant in both developing and setting parameters of permutation-based similarity searching approaches.