A compact index for order‐preserving pattern matching

Abstract

Summary Order‐preserving pattern matching has been introduced recently, but it has already attracted much attention. Given a reference sequence and a pattern, we want to locate all substrings of the reference sequence whose elements have the same relative order as the pattern elements. For this problem, we consider the offline version in which we build an index for the reference sequence so that subsequent searches can be completed very efficiently. We propose a space‐efficient index that works well in practice despite its lack of good worst‐case time bounds. Our solution is based on the new approach of decomposing the indexed sequence into an order component, containing ordering information, and a δ component, containing information on the absolute values. Experiments show that this approach is viable, is faster than the available alternatives, and is the first one offering simultaneously small space usage and fast retrieval.

String periods in the order-preserving model

“…Other developments in this area include a multiple-pattern matching algorithm for the op-model [33], an approximate version of op-pattern matching [29], compressed index constructions [13,22], a small-space index for op-pattern matching that supports only short queries [28], and a number of practical approaches [9,11,12,14,24].…”