Efficiently Approximating Edit Distance Between Pseudorandom Strings

Kuszmaul, William

doi:10.1137/1.9781611975482.71

Cited by 10 publications

(13 citation statements)

References 23 publications

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“…What do we know in the two strings case? : Let us contrast this result to what is known for m = 2 case [AK12, Kus19,BSS20]. When one of the two strings is (p, B)-pseudorandom, Kuszmaul gave an algorithm that runs in time Õ(nB) time but only computes an O( 1 p ) approximation to edit distance [Kus19].…”

Section: Contributionsmentioning

confidence: 91%

Approximating LCS and Alignment Distance over Multiple Sequences

Das¹,

Saha²

2021

Preprint

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We study the problem of aligning multiple sequences with the goal of finding an alignment that either maximizes the number of aligned symbols (the longest common subsequence (LCS) problem), or minimizes the number of unaligned symbols (the alignment distance aka the complement of LCS). Multiple sequence alignment is a well-studied problem in bioinformatics and is used routinely to identify regions of similarity among DNA, RNA, or protein sequences to detect functional, structural, or evolutionary relationships among them. It is known that exact computation of LCS or alignment distance of m sequences each of length n requires Θ(n m ) time unless the Strong Exponential Time Hypothesis is false. However, unlike the case of two strings, fast algorithms to approximate LCS and alignment distance of multiple sequences is lacking in the literature. In this paper, we make significant progress towards that direction.• If the LCS of m sequences each of length n is λn for some λ ∈ [0, 1], then in Õm (n m 2 +1 ) 1 time, we can return a common subsequence of length at least λ 2 n

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Section: Contributionsmentioning

confidence: 91%

Approximating LCS and Alignment Distance over Multiple Sequences

Das¹,

Saha²

2021

Preprint

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“…A sublinear time algorithm was also recently developed in [GKS19]; see also earlier [BJKK04], and the aforementioned [BEK + 03]. Another related line of work has been on computing edit distance for the semirandom models of input [AK12,Kus19]. Parallel (MPC) algorithms were developed in [BEG + 18, HSS19].…”

Section: Related Workmentioning

confidence: 99%

Edit Distance in Near-Linear Time: it's a Constant Factor

Andoni¹,

Nosatzki²

2020

Preprint

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We present an algorithm for approximating the edit distance between two strings of length n in time n 1+ , for any > 0, up to a constant factor. Our result completes the research direction set forth in the recent breakthrough paper [CDG + 18], which showed the first constant-factor approximation algorithm with a (strongly) sub-quadratic running time. Several recent results have shown near-linear complexity under different restrictions on the inputs (eg, when the edit distance is close to maximal, or when one of the inputs is pseudo-random). In contrast, our algorithm obtains a constant-factor approximation in near-linear running time for any input strings.

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“…Further work has resulted in near-linear algorithms to approximate the edit distance for several special cases [14,18,34,42,43].…”

Section: Related Workmentioning

confidence: 99%

Approximate Similarity Search Under Edit Distance Using Locality-Sensitive Hashing

McCauley

2019

Preprint

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Edit distance similarity search, also called approximate pattern matching, is a fundamental problem with widespread applications. The goal of the problem is to preprocess n strings of length d, to quickly answer queries q of the form: if there is a database string within edit distance r of q, return a database string within edit distance cr of q. A data structure solving this problem is analyzed using two criteria: the amount of extra space used in preprocessing, and the expected time to answer a query.Previous approaches to this problem have either used trie-based methods, which give exact solutions at the cost of expensive queries, or embeddings, which only work for large (superconstant) values of c.In this work we achieve the first bounds for any approximation factor c, via a simple and easyto-implement hash function. This gives a running time of O(d3 r n 1/c ), with space O(3 r n 1+1/c + dn). We show how to apply these ideas to the closely-related Approximate Nearest Neighbor problem for edit distance, obtaining similar time bounds.

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Efficiently Approximating Edit Distance Between Pseudorandom Strings

Cited by 10 publications

References 23 publications

Approximating LCS and Alignment Distance over Multiple Sequences

Approximating LCS and Alignment Distance over Multiple Sequences

Edit Distance in Near-Linear Time: it's a Constant Factor

Approximate Similarity Search Under Edit Distance Using Locality-Sensitive Hashing

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