Order-Preserving Incomplete Suffix Trees and Order-Preserving Indexes

Recently Kubica et al. (Inf. Process. Let., 2013) and Kim et al. (submitted to Theor. Comp. Sci.) introduced order-preserving pattern matching: for a given text the goal is to find its factors having the same “shape” as a given pattern. The known results include a linear-time algorithm for this problem (in case of polynomially-bounded alphabet) and a generalization to multiple patterns. We extend these results and give an O(n log log n) time construction of an index that enables orderpreserving pattern matching queries in time linear with respect to the length of the pattern. The main novel component is a data structure being an incomplete suffix tree in the order-preserving setting. The tree can miss single letters related to branchings at internal nodes. Such incompleteness results from the weakness of our so called weak character oracle. However, due to its weakness, such oracle can be computed in O(log logn) time on-line using a sliding-window approach. For most of the applications such incomplete suffix-trees provide the same functional power as the complete ones. We also give an O( n logn log logn ) time algorithm constructing complete order-preserving suffix trees. ? Supported by the NSF–funded iPlant Collaborative (NSF grant #DBI-0735191). ?? Supported by grant no. N206 566740 of the National Science Centre.