Pattern Matching with Flexible Wildcards

Abstract

Pattern matching with wildcards (PMW) has great theoretical and practical significance in bioinformatics, information retrieval, and pattern mining. Due to the uncertainty of wildcards, not only is the number of all matches exponential with respect to the maximal gap flexibility and the pattern length, but the matching positions in PMW are also hard to choose. The objective to count the maximal number of matches one by one is computationally infeasible. Therefore, rather than solving the generic PMW problem, many research efforts have further defined new problems within PMW according to different application backgrounds. To break through the limitations of either fixing the number or allowing an unbounded number of wildcards, pattern matching with flexible wildcards (PMFW) allows the users to control the ranges of wildcards. In this paper, we provide a survey on the state-of-the-art algorithms for PMFW, with detailed analyses and comparisons, and discuss challenges and opportunities in PMFW research and applications.

Frequent State Transition Patterns of Multivariate Time Series

“…The occurrence of STAP can be directly obtained by looking up the list. The time delays in STAP, also called periodic wildcard gaps [44]- [47] coincide with that of DTA when the lower bound equals 0.…”

“…i.e., ∅ matches the MTS at any time point, it is called a wildcard. For univariate time series, a wildcard [44], [45], [47] (also called a not cared position) matches any character which is time point in an MTS. To judge whether or not state s is frequent in S, we need to calculate its support, which is given by Sup(s, S) = t∈T m(S, t, s)…”

Strict pattern matching under non-overlapping condition

“…Diverse pattern matching methods have been investigated such as string similarity search [12], windowed subsequence matching [13], circular string matching [14], approximate string matching [15], and string searching in large spatial databases [16]. Recently, a new kind of wildcard, named gap constraint (or flexible wildcard [17,18]), is widely used in the tasks of pattern matching [19] and sequential pattern mining [20,21], since it is not only more flexible than traditional wildcards such as "?" and "*", but also more easy to meet users' requirements.…”