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A Simple Sublinear Algorithm for Gap Edit Distance [article]

Joshua Brakensiek and Moses Charikar and Aviad Rubinstein
<span title="2020-07-28">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Our main result is a very simple algorithm for this benchmark that runs in time Õ(n/√(k)), and in particular settles the open problem of obtaining a truly sublinear time for the entire range of relevant  ...  While exact computation in the worst case is believed to require near-quadratic time, previous work showed that in certain regimes it is possible to solve the following gap edit distance problem in sub-linear  ...  Gap Edit Distance: k vs k 2 We give new approximation algorithms for edit distance that run in sublinear time when the input strings are close.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.14368v1">arXiv:2007.14368v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oe6kb6h7rff5vmepdgrebyivzy">fatcat:oe6kb6h7rff5vmepdgrebyivzy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200809084654/https://arxiv.org/pdf/2007.14368v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.14368v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Improved Sublinear-Time Edit Distance for Preprocessed Strings [article]

Karl Bringmann, Alejandro Cassis, Nick Fischer, Vasileios Nakos
<span title="2022-04-29">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We study the problem of approximating the edit distance of two strings in sublinear time, in a setting where one or both string(s) are preprocessed, as initiated by Goldenberg, Rubinstein, Saha (STOC '  ...  Specifically, in the (k, K)-gap edit distance problem, the goal is to distinguish whether the edit distance of two strings is at most k or at least K.  ...  comparison of sublinear-time algorithms for the (k, k • g)-gap edit distance problem for different gap parameters g.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2204.14137v1">arXiv:2204.14137v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yqwslcomenggbfe5z4jyr76hpu">fatcat:yqwslcomenggbfe5z4jyr76hpu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220504061247/https://arxiv.org/pdf/2204.14137v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f8/c4/f8c4234118f7aa2a4eeb1d19fbf00086c112112e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2204.14137v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Almost-Optimal Sublinear-Time Edit Distance in the Low Distance Regime [article]

Karl Bringmann, Alejandro Cassis, Nick Fischer, Vasileios Nakos
<span title="2022-02-16">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Our result also reveals a surprising similarity of Hamming distance and edit distance in the low distance regime: For both, the (k,k^1+o(1))-gap problem has time complexity n/k^1± o(1) for small k.  ...  We revisit the task of computing the edit distance in sublinear time.  ...  As a sanity check, let us confirm that an algorithm for the Tree Distance Problem can distinguish edit distances with a polylogarithmic gap.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2202.08066v1">arXiv:2202.08066v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/eh356oj2h5apbo5urrmutd5hjm">fatcat:eh356oj2h5apbo5urrmutd5hjm</a> </span>
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Sublinear-Time Algorithms for Computing Embedding Gap Edit Distance [article]

Tomasz Kociumaka, Barna Saha
<span title="2020-07-24">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we design new sublinear-time algorithms for solving the gap edit distance problem and for embedding edit distance to Hamming distance.  ...  For the gap edit distance problem, we give a greedy algorithm that distinguishes in time Õ(n/k+k^2) between length-n input strings with edit distance at most k and those with edit distance more than 4k  ...  We give a simple greedy algorithm solving the quadratic gap edit distance problem inÕ( n k + k 2 ) time.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.12762v1">arXiv:2007.12762v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/eybde5do6ngjznx3uyhzi4srai">fatcat:eybde5do6ngjznx3uyhzi4srai</a> </span>
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Algorithmic Advances for Searching Biosequence Databases [chapter]

Eugene W. Myers
<span title="">1994</span> <i title="Springer US"> Computational Methods in Genome Research </i> &nbsp;
K-Tuple Measure An algorithm by Ukkonen [16] centers on using the k-tuple measure between strings to serve as a lower bound on their simple Levenshtein distance.  ...  Thinking of insertions, deletions, and mismatches as editing operations that transform one sequence to another, one defines the simple Levenshtein distance [7] , S(V, W), as the minimum number of such  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-1-4615-2451-9_10">doi:10.1007/978-1-4615-2451-9_10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cvl4eygyovcynebnmqtnezgx2a">fatcat:cvl4eygyovcynebnmqtnezgx2a</a> </span>
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Sublinear Algorithms for Gap Edit Distance [article]

Elazar Goldenberg, Robert Krauthgamer, Barna Saha
<span title="2019-10-02">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A simple dynamic programming computes the edit distance between two strings of length n in O(n^2) time, and a more sophisticated algorithm runs in time O(n+t^2) when the edit distance is t [Landau, Myers  ...  We study sublinear-time algorithms for small edit distance, which was investigated extensively because of its numerous applications.  ...  These applications can benefit from super-fast algorithms that answer whether the edit distance is below a threshold t or above f (t) for some function f , known as the gap edit distance problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.00901v1">arXiv:1910.00901v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bo7ifg6synavfcagnvjbsp7t7y">fatcat:bo7ifg6synavfcagnvjbsp7t7y</a> </span>
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The smoothed complexity of edit distance

Alexandr Andoni, Robert Krauthgamer
<span title="2012-09-01">2012</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xjsyokeq6nawdowtypazhyoyli" style="color: black;">ACM Transactions on Algorithms</a> </i> &nbsp;
The first algorithm runs in near-linear time, namely d 1+ε for any fixed ε > 0. The second one runs in time sublinear in d, assuming the edit distance is not too small.  ...  We are thus able to build on algorithms developed for the Ulam metric, whose much better algorithmic guarantees usually do not carry over to general edit distance.  ...  We thank Dick Karp for useful discussions at an early stage of this research.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2344422.2344434">doi:10.1145/2344422.2344434</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/636p4kt4k5ee5b3ju4asfwwjci">fatcat:636p4kt4k5ee5b3ju4asfwwjci</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170921210900/http://www.mit.edu/%7Eandoni/papers/smooth.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/55/e0/55e09d8d2885b506427894c638b3bb93947d37a2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2344422.2344434"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

The Smoothed Complexity of Edit Distance [chapter]

Alexandr Andoni, Robert Krauthgamer
<span title="">2008</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
The first algorithm runs in near-linear time, namely d 1+ε for any fixed ε > 0. The second one runs in time sublinear in d, assuming the edit distance is not too small.  ...  We are thus able to build on algorithms developed for the Ulam metric, whose much better algorithmic guarantees usually do not carry over to general edit distance.  ...  We thank Dick Karp for useful discussions at an early stage of this research.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-70575-8_30">doi:10.1007/978-3-540-70575-8_30</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7gmflpyfcrbhbawnkytelmb7du">fatcat:7gmflpyfcrbhbawnkytelmb7du</a> </span>
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Nested Dataflow Algorithms for Dynamic Programming Recurrences with more than O(1) Dependency [article]

Yuan Tang
<span title="2019-11-13">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
sublinear-time GAP algorithm based on the closure method and Nested Dataflow method. % We also improve the time bounds of classic work-efficient, cache-oblivious and cache-efficient algorithms for the  ...  In 1994, Galil and Park developed work-efficient and sublinear-time algorithms for several important dynamic programming problems based on the closure method and matrix product method.  ...  They Shanghai Natural Science Funding (No. 18ZR1403100) raised an open problem in their paper if there exists a better algorithm for the general edit distance problem when allowing gaps of insertions  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1911.05333v1">arXiv:1911.05333v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/s2ftachyofabzpogg2co26m23e">fatcat:s2ftachyofabzpogg2co26m23e</a> </span>
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Periodicity testing with sublinear samples and space

Funda Ergun, S. Muthukrishnan, Cenk Sahinalp
<span title="2010-03-01">2010</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xjsyokeq6nawdowtypazhyoyli" style="color: black;">ACM Transactions on Algorithms</a> </i> &nbsp;
Our algorithms may be viewed as working on streaming inputs where each data item is seen once and in order, storing only a sublinear -O( √ n polylog n) -size sample from which periodicities are identified  ...  In this work, we are interested in finding representative trends in long large data streams in the presence of computational constraints; to this end we present algorithms for discovering periodic trends  ...  Acknowledgements The authors would like to thank the anonymous referees for significantly improving the presentation of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1721837.1721859">doi:10.1145/1721837.1721859</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kbxo32bbyberzbkrjubbpldzj4">fatcat:kbxo32bbyberzbkrjubbpldzj4</a> </span>
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A sublinear algorithm for weakly approximating edit distance

Tugkan Batu, Funda Ergün, Joe Kilian, Avner Magen, Sofya Raskhodnikova, Ronitt Rubinfeld, Rahul Sami
<span title="">2003</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jlc5kugafjg4dl7ozagimqfcbm" style="color: black;">Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC &#39;03</a> </i> &nbsp;
Our algorithm for testing the edit distance works by recursively subdividing the strings A and B into smaller substrings and looking for pairs of substrings in A, B with small edit distance.  ...  We show how to determine whether the edit distance between two given strings is small in sublinear time.  ...  In fact, we give (to our knowledge) the first sublinear time algorithm for approximating the edit distance in the following sense.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/780542.780590">doi:10.1145/780542.780590</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/stoc/BatuEKMRRS03.html">dblp:conf/stoc/BatuEKMRRS03</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6g2nhgh45bg6vbpzhubc4rjzka">fatcat:6g2nhgh45bg6vbpzhubc4rjzka</a> </span>
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A sublinear algorithm for weakly approximating edit distance

Tugkan Batu, Funda Ergün, Joe Kilian, Avner Magen, Sofya Raskhodnikova, Ronitt Rubinfeld, Rahul Sami
<span title="">2003</span> <i title="ACM Press"> Proceedings of the thirty-fifth ACM symposium on Theory of computing - STOC &#39;03 </i> &nbsp;
Our algorithm for testing the edit distance works by recursively subdividing the strings A and B into smaller substrings and looking for pairs of substrings in A, B with small edit distance.  ...  We show how to determine whether the edit distance between two given strings is small in sublinear time.  ...  In fact, we give (to our knowledge) the first sublinear time algorithm for approximating the edit distance in the following sense.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/780587.780590">doi:10.1145/780587.780590</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6nlkb2j4wfhlzdh64wspvxocue">fatcat:6nlkb2j4wfhlzdh64wspvxocue</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170812201708/http://www.cs.princeton.edu/courses/archive/spr04/cos598B/bib/BatuEKMRR.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f0/c2/f0c25fcd043ac5cacf6f63a1d030e1d6b4705eb1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/780587.780590"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Does Preprocessing help in Fast Sequence Comparisons? [article]

Elazar Goldenberg, Aviad Rubinstein, Barna Saha
<span title="2021-08-20">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Interestingly, by combining ideas from our algorithms with preprocessing, we provide new improved results for approximating edit distance without preprocessing in subquadratic time.  ...  Small edit distance: For general strings, if their edit distance is at most k, we can compute it exactly with O(nlog(n)) preprocessing and O(k^2 log(n)) query time.  ...  We remark that another related hardness result is known for the case where we only preprocess one string: Abboud and Vassilevska-Williams show that, assuming a nonuniform variant of SETH, even polynomial  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2108.09115v1">arXiv:2108.09115v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/unknlsp54nhjxiv4pbcxsp435a">fatcat:unknlsp54nhjxiv4pbcxsp435a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210829182638/https://arxiv.org/pdf/2108.09115v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/8f/d3/8fd36ecef85e51ba5bd68296d422f4637d85d5ab.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2108.09115v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Approximating Edit Distance in Truly Subquadratic Time: Quantum and MapReduce [article]

Mahdi Boroujeni and Soheil Ehsani and Mohammad Ghodsi and MohammadTaghi HajiAghayi and Saeed Seddighin
<span title="2018-04-25">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
To this end, we provide a MapReduce algorithm to approximate edit distance within a factor of 3, with sublinearly many machines and sublinear memory.  ...  Our main result is a quantum constant approximation algorithm for computing the edit distance in truly subquadratic time.  ...  Acknowledgment We would like to thank Andrew Childs, Omid Etesami, Salman Beigi, and Mohammad Ali Abam for their comments on an earlier version of the paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1804.04178v2">arXiv:1804.04178v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ij3ko4ecvrfexoywajetqvjoj4">fatcat:ij3ko4ecvrfexoywajetqvjoj4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200826095019/https://arxiv.org/pdf/1804.04178v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c9/3b/c93bc33456c29d8320f95e668b7147a49a1aa6f6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1804.04178v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Embedding the Ulam metric into l 1

Moses Charikar, Robert Krauthgamer
<span title="">2006</span> <i title="Theory of Computing Exchange"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fu3pndsuo5dpngr3be4mroohd4" style="color: black;">Theory of Computing</a> </i> &nbsp;
Although the minimum distortion required to embed edit distance into 1 has received a lot of attention lately, there is a large gap between known upper and lower bounds.  ...  A very powerful paradigm is to map the metric space induced by the edit distance into a normed space (e. g., 1 ) with small distortion, and then use the rich algorithmic toolkit known for normed spaces  ...  Acknowledgements We thank the anonymous reviewers for helpful comments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4086/toc.2006.v002a011">doi:10.4086/toc.2006.v002a011</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/journals/toc/CharikarK06.html">dblp:journals/toc/CharikarK06</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lvsk4ba6mrcr7airm5lcrigham">fatcat:lvsk4ba6mrcr7airm5lcrigham</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20181119200557/http://www.theoryofcomputing.org/articles/v002a011/v002a011.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/86/9b/869bf5b86f8d586b97fdced87a8acad767bb0542.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4086/toc.2006.v002a011"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>
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