Combinatorial Algorithms for Subsequence Matching: A Survey

Abstract

In this paper we provide an overview of a series of recent results regarding algorithms for searching for subsequences in words or for the analysis of the sets of subsequences occurring in a word.

The k-Centre Problem for Classes of Cyclic Words

“…Informally, a subsequence of a word w is a word u that can be found by deleting some subset of the symbols w. Subsequences are a heavily studied object within computer science [Bar+20; Day+21; Fle+22; HSZ17; Kos+21; Lot97; MSY04; Sim03; Tro03; Zet16] and beyond, with applications in a wide number of fields including bioinformatics [HWG20; Shi+19], database theory [Art+17], and modelling concurrency [Sha78]. A recent survey of subsequence algorithms has been provided by Kosche et al [Kos+22], highlighting major results for problems on funding subsequences in words.…”

Matching Patterns with Variables in Approximate Settings

“…< i |u| ≤ |w| with w[i j ] = u[ j] for all j ∈ [|u|]. Subsequences are also a heavily investigated topic in the area of word combinatorics, string algorithms, and combinatorial pattern matching, and are connected to other areas of computer science (see, e.g., in the Chapter Subwords by J. Sakarovitch and I. Simon of the standard textbook [123] or the survey [107] and the references therein). In theoretical computer science, one can often encounter subsequences and their generalizations; for instance, in logic of automata theory, subsequences are used in the context of piecewise testability [156,157], in particular, to the height of piecewise testable languages [94,95,96], subword order [84,113,112], or downward closures [167].…”