Approximating Approximate Pattern Matching
arXiv: Data Structures and Algorithms(2018)
摘要
Given a text T of length n and a pattern P of length m, the approximate pattern matching problem asks for computation of a particular distance function between P and every m-substring of T. We consider a (1±ε) multiplicative approximation variant of this problem, for ℓ_p distance function. In this paper, we describe two (1+ε)-approximate algorithms with a runtime of O(n/ε) for all (constant) non-negative values of p. For constant p ≥ 1 we show a deterministic (1+ε)-approximation algorithm. Previously, such run time was known only for the case of ℓ_1 distance, by Gawrychowski and Uznański [ICALP 2018] and only with a randomized algorithm. For constant 0 ≤ p ≤ 1 we show a randomized algorithm for the ℓ_p, thereby providing a smooth tradeoff between algorithms of Kopelowitz and Porat [FOCS 2015, SOSA 2018] for Hamming distance (case of p=0) and of Gawrychowski and Uznański for ℓ_1 distance.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络