Dictionary matching and indexing with errors and don't cares

Abstract

This paper considers various flavors of the following online problem: preprocess a text or collection of strings, so that given a query string p, all matches of p with the text can be reported quickly.In this paper we consider matches in which a bounded number of mismatches are allowed, or in which a bounded number of "don't care" characters are allowed.The specific problems we look at are: indexing, in which there is a single text t, and we seek locations where p matches a substring of t; dictionary queries, in which a collection of strings is given upfront, and we seek those strings which match p in their entirety; and dictionary matching, in which a collection of strings is given upfront, and we seek those substrings of a (long) p which match an original string in its entirety. These are all instances of an all-to-all matching problem, for which we provide a single solution.The performance bounds all have a similar character. For example, for the indexing problem with n = |t| and m = |p|, the query time for k substitutions is O(m + (c 1 log n) k k! + # matches), with a data structure of size O(n (c 2 log n) k k! ) and a preprocessing time of O(n (c 2 log n) k k!), where c1, c2 > 1 are constants. The deterministic preprocessing assumes a weakly nonuniform RAM model; this assumption is not needed if randomization is used in the preprocessing.

Weighted Ancestors in Suffix Trees

“…The improvement can be also embedded in the extensions. Searching Substrings Internally in the Suffix Tree Cole et al [7], when proposing data structures for indexing a text w[1..n] with k mismatches, k errors and k wildcards, suggested the LCP data structure. The LCP data structure comes in two variants, rooted LCP and unrooted LCP.…”

String Data Structures for Computational Molecular Biology

“…can be supported for a pattern p plus a time complexity equal to the size of the output. Using techniques presented in [22], the structure can be modified to solve the problem in O(nm log(nm) + n(c 1 log n) k+1 /k!) preprocessing time, and O(m + (c 2 log n) k log log n) query time (c 1 and c 2 are constants); this approach is worse than the trie approach for small values of .…”

Indexing a sequence for mapping reads with a single mismatch

“…There exist some solutions avoiding the convolution method as well [18][19][20]. A number of solutions exist in the literature that consider the problem of text indexing with don't cares [21][22][23][24]. Notably, in the literature, the don't cares are also referred to as wildcards.…”