Theoretical Computer Science ( IF 0.747 ) Pub Date : 2020-11-20 , DOI: 10.1016/j.tcs.2020.11.036 Arnab Ganguly; Wing-Kai Hon; Kunihiko Sadakane; Rahul Shah; Sharma V. Thankachan; Yilin Yang
Let be a collection of d patterns of total length n characters, which are chosen from an alphabet Σ of size σ. Given a text T (over Σ), the dictionary indexing problem is to create a data structure using which we can report all positions j (called occurrences) where at least one of the patterns is a match with the same-length substring of T that starts at j. We consider this problem under the following definitions of matching.
Parameterized Matching: The characters of Σ are partitioned into static characters and parameterized characters. Two equal length strings S and are a parameterized match iff the static characters match exactly, and there exists a one-to-one function which renames the parameterized characters in S to those in .
Order-Preserving Matching: The alphabet Σ is ordered. Two equal length strings S and are an order-preserving match iff for any two integers , , where ≺ denotes the precedence order in Σ.