Average-Case Optimal Approximate Circular String Matching

Abstract

Abstract. Approximate string matching is the problem of finding all factors of a text t of length n that are at a distance at most k from a pattern x of length m. Approximate circular string matching is the problem of finding all factors of t that are at a distance at most k from x or from any of its rotations. In this article, we present a new algorithm for approximate circular string matching under the edit distance model with optimal average-case search time O(n(k + log m)/m). Optimal averagecase search time can also be achieved by the algorithms for multiple approximate string matching (Fredriksson and Navarro, 2004) using x and its rotations as the set of multiple patterns. Here we reduce the preprocessing time and space requirements compared to that approach.

Dynamic RLE-Compressed Edit Distance Tables Under General Weighted Cost Functions

“…Note that ed 1 (A, B) essentially corresponds to the minimum number of edit operations required in transforming A into B. For example ed 1 (apple, carpe) = 3 and an optimal three-operation way to transform A = apple into B = carpe is to delete A [4] = l, substitute A[2] = p by r and insert the character c to the front. Throughout the paper let m denote the length of A and n denote the length of B.…”

Quasi-Linear-Time Algorithm for Longest Common Circular Factor

“…Just as the LCF problem was an extension of the classical pattern matching, the LCCF can be seen as an extension of the circular pattern matching problem. The latter can still be solved in linear time using the suffix tree and admits a number of efficient solutions based on practical approaches [4,9,16,20,25,28], also in the approximate variant [6,7,17,19], as well as an indexing variants [3,20,21], and the problem of detecting various circular patterns [26]. The LCCF problem is further related to the notion of unbalanced translocations [8,10,27,29,30].…”

Circular Pattern Matching with k Mismatches

“…In many real-world applications, such as in bioinformatics [4,22,25,7] or in image processing [3,33,34,32], any cyclic shift (rotation) of P is a relevant pattern, and thus one is interested in computing the minimal distance of every length-m substring of T and any cyclic shift of P , if this distance is no more than k. This is the circular pattern matching with k mismatches (k-CPM) problem. A multitude of papers [17,8,6,5,9,24] have thus been devoted to solving the k-CPM problem but, to the best of our knowledge, only average-case upper bounds are known; i.e. in these works the assumption is that text T is uniformly random.…”