Streaming k-mismatch with error correcting and applications

Radoszewski, Jakub; Starikovskaya, Tatiana

doi:10.1016/j.ic.2019.104513

Cited by 7 publications

(4 citation statements)

References 26 publications

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“…We pay our attention to communication complexity of string problems where the inputs A and B are strings over an alphabet Σ. Communication complexity of string problems has played a critical role in the space lower bound analysis of several streaming processing problems including Hamming/edit/swap distances [2], pattern matching with k-mismatches [3], parameterized pattern matching [4], dictionary matching [5], and quasiperiodicity [6].…”

Section: Introductionmentioning

confidence: 99%

Compressed Communication Complexity of Hamming Distance

et al. 2021

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We consider the communication complexity of the Hamming distance of two strings. Bille et al. [SPIRE 2018] considered the communication complexity of the longest common prefix (LCP) problem in the setting where the two parties have their strings in a compressed form, i.e., represented by the Lempel-Ziv 77 factorization (LZ77) with/without self-references. We present a randomized public-coin protocol for a joint computation of the Hamming distance of two strings represented by LZ77 without self-references. Although our scheme is heavily based on Bille et al.’s LCP protocol, our complexity analysis is original which uses Crochemore’s C-factorization and Rytter’s AVL-grammar. As a byproduct, we also show that LZ77 with/without self-references are not monotonic in the sense that their sizes can increase by a factor of 4/3 when a prefix of the string is removed.

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Section: Introductionmentioning

confidence: 99%

Compressed Communication Complexity of Hamming Distance

et al. 2021

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“…In that model, the text arrives in a stream, one character at a time, and the goal is to compute, or estimate, after the arrival of each text character, the Hamming distance between P and the current suffix of T . The state-of-the-art exact algorithm [15] uses Õ(k) space and costs Õ( √ k) time per character, which improves upon [14,23,36,38]. A recent approximate streaming algorithm [12] uses Õ(min(ε −2 √ k, ε −1.5 √ n)) space and costs Õ(ε −3 ) time per character, which improves upon [16,39].…”

Section: Related Workmentioning

confidence: 99%

Improved Circular $k$-Mismatch Sketches

Golan,

Kociumaka,

Kopelowitz

et al. 2020

Preprint

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The shift distance sh(S 1 , S 2 ) between two strings S 1 and S 2 of the same length is defined as the minimum Hamming distance between S 1 and any rotation (cyclic shift) of S 2 . We study the problem of sketching the shift distance, which is the following communication complexity problem: Strings S 1 and S 2 of length n are given to two identical players (encoders), who independently compute sketches (summaries) sk(S 1 ) and sk(S 2 ), respectively, so that upon receiving the two sketches, a third player (decoder) is able to compute (or approximate) sh(S 1 , S 2 ) with high probability.This paper primarily focuses on the more general k-mismatch version of the problem, where the decoder is allowed to declare a failure if sh(S 1 , S 2 ) > k, where k is a parameter known to all parties. Andoni et al. (STOC'13) introduced exact circular k-mismatch sketches of size Õ(k + D(n)), where D(n) is the number of divisors of n. Andoni et al. also showed that their sketch size is optimal in the class of linear homomorphic sketches.We circumvent this lower bound by designing a (non-linear) exact circular k-mismatch sketch of size Õ(k); this size matches communication-complexity lower bounds. We also design (1 ± ε)approximate circular k-mismatch sketch of size Õ(min(ε −2 √ k, ε −1.5 √ n)), which improves upon an Õ(ε −2 √ n)-size sketch of Crouch and McGregor (APPROX'11).

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“…Related to our work is the problem of streaming pattern matching, where the goal is to find all occurrences of a pattern (possibly with some bounded number mismatches) in a data stream, see e.g. [65,80,56,53,19,20,21,22,23,57,59,58,78,84] and search of repetitions in streams [33,31,32,52,51,72,73].…”

Section: Regmentioning

confidence: 99%

Sliding Window Algorithms for Regular Languages

Ganardi

Hucke

Lohrey

2018

Language and Automata Theory and Applications

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We study the problem of recognizing regular languages in a variant of the streaming model of computation, called the sliding window model. In this model, we are given a size of the sliding window n and a stream of symbols. At each time instant, we must decide whether the suffix of length n of the current stream ("the active window") belongs to a given regular language.Recent works [14,15] showed that the space complexity of an optimal deterministic sliding window algorithm for this problem is either constant, logarithmic or linear in the window size n and provided natural language theoretic characterizations of the space complexity classes. Subsequently, [16] extended this result to randomized algorithms to show that any such algorithm admits either constant, double logarithmic, logarithmic or linear space complexity.In this work, we make an important step forward and combine the sliding window model with the property testing setting, which results in ultra-efficient algorithms for all regular languages. Informally, a sliding window property tester must accept the active window if it belongs to the language and reject it if it is far from the language. We consider deterministic and randomized sliding window property testers with onesided and two-sided errors. In particular, we show that for any regular language, there is a deterministic sliding window property tester that uses logarithmic space and a randomized sliding window property tester with two-sided error that uses constant space.

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Streaming k-mismatch with error correcting and applications

Cited by 7 publications

References 26 publications

Compressed Communication Complexity of Hamming Distance

Compressed Communication Complexity of Hamming Distance

Improved Circular $k$-Mismatch Sketches

Sliding Window Algorithms for Regular Languages

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