A Framework for Dynamic Parameterized Dictionary Matching

Two equal-length strings S and S′ are a parameterized-match (p-match) iff there exists a one-toone function that renames the characters in S to those in S′. Let P be a collection of d patterns of total length n characters that are chosen from an alphabet Σ of cardinality σ. The task is to index P such that we can support the following operations: search(T ): given a text T , report all occurrences 〈j, Pi〉 such that there exists a pattern Pi ∈ P that is a p-match with the substring T [j, j + |Pi| − 1]. insert(Pi)/delete(Pi): modify the index when a pattern Pi is inserted/deleted. We present a linear-space index that occupies O(n logn) bits and supports (i) search(T ) in worstcase O(|T | log2 n+ occ) time, where occ is the number of occurrences reported, and (ii) insert(Pi) and delete(Pi) in amortized O(|Pi|polylog(n)) time. Then, we present a succinct index that occupies (1+o(1))n log σ+O(d logn) bits and supports (i) search(T ) in worst-case O(|T | log2 n+ occ) time, and (ii) insert(Pi) and delete(Pi) in amortized O(|Pi|polylog(n)) time. We also present results related to the semi-dynamic variant of the problem, where deletion is not allowed. 1998 ACM Subject Classification F.2.2 Pattern Matching