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Documents authored by Clifford, Raphaël

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Clifford, Raphael

Document
DOI: 10.4230/LIPIcs.CPM.2022.18
The Dynamic k-Mismatch Problem

Authors: Raphaël Clifford, Paweł Gawrychowski, Tomasz Kociumaka, Daniel P. Martin, and Przemysław Uznański

Published in: LIPIcs, Volume 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)

Abstract
The text-to-pattern Hamming distances problem asks to compute the Hamming distances between a given pattern of length m and all length-m substrings of a given text of length n ≥ m. We focus on the well-studied k-mismatch version of the problem, where a distance needs to be returned only if it does not exceed a threshold k. Moreover, we assume n ≤ 2m (in general, one can partition the text into overlapping blocks). In this work, we develop data structures for the dynamic version of the k-mismatch problem supporting two operations: An update performs a single-letter substitution in the pattern or the text, whereas a query, given an index i, returns the Hamming distance between the pattern and the text substring starting at position i, or reports that the distance exceeds k. First, we describe a simple data structure with 𝒪̃(1) update time and 𝒪̃(k) query time. Through considerably more sophisticated techniques, we show that 𝒪̃(k) update time and 𝒪̃(1) query time is also achievable. These two solutions likely provide an essentially optimal trade-off for the dynamic k-mismatch problem with m^{Ω(1)} ≤ k ≤ √m: we prove that, in that case, conditioned on the 3SUM conjecture, one cannot simultaneously achieve k^{1-Ω(1)} time for all operations (updates and queries) after n^{𝒪(1)}-time initialization. For k ≥ √m, the same lower bound excludes achieving m^{1/2-Ω(1)} time per operation. This is known to be essentially tight for constant-sized alphabets: already Clifford et al. (STACS 2018) achieved 𝒪̃(√m) time per operation in that case, but their solution for large alphabets costs 𝒪̃(m^{3/4}) time per operation. We improve and extend the latter result by developing a trade-off algorithm that, given a parameter 1 ≤ x ≤ k, achieves update time 𝒪̃(m/k +√{mk/x}) and query time 𝒪̃(x). In particular, for k ≥ √m, an appropriate choice of x yields 𝒪̃(∛{mk}) time per operation, which is 𝒪̃(m^{2/3}) when only the trivial threshold k = m is provided.
Cite as

Raphaël Clifford, Paweł Gawrychowski, Tomasz Kociumaka, Daniel P. Martin, and Przemysław Uznański. The Dynamic k-Mismatch Problem. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 18:1-18:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{clifford_et_al:LIPIcs.CPM.2022.18,
  author =	{Clifford, Rapha\"{e}l and Gawrychowski, Pawe{\l} and Kociumaka, Tomasz and Martin, Daniel P. and Uzna\'{n}ski, Przemys{\l}aw},
  title =	{{The Dynamic k-Mismatch Problem}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{18:1--18:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-234-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{223},
  editor =	{Bannai, Hideo and Holub, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.18},
  URN =		{urn:nbn:de:0030-drops-161454},
  doi =		{10.4230/LIPIcs.CPM.2022.18},
  annote =	{Keywords: Pattern matching, Hamming distance, dynamic algorithms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.66
RLE Edit Distance in Near Optimal Time

Authors: Raphaël Clifford, Paweł Gawrychowski, Tomasz Kociumaka, Daniel P. Martin, and Przemysław Uznański

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
We show that the edit distance between two run-length encoded strings of compressed lengths m and n respectively, can be computed in O(mn log(mn)) time. This improves the previous record by a factor of O(n/log(mn)). The running time of our algorithm is within subpolynomial factors of being optimal, subject to the standard SETH-hardness assumption. This effectively closes a line of algorithmic research first started in 1993.
Cite as

Raphaël Clifford, Paweł Gawrychowski, Tomasz Kociumaka, Daniel P. Martin, and Przemysław Uznański. RLE Edit Distance in Near Optimal Time. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 66:1-66:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{clifford_et_al:LIPIcs.MFCS.2019.66,
  author =	{Clifford, Rapha\"{e}l and Gawrychowski, Pawe{\l} and Kociumaka, Tomasz and Martin, Daniel P. and Uzna\'{n}ski, Przemys{\l}aw},
  title =	{{RLE Edit Distance in Near Optimal Time}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{66:1--66:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.66},
  URN =		{urn:nbn:de:0030-drops-110109},
  doi =		{10.4230/LIPIcs.MFCS.2019.66},
  annote =	{Keywords: String algorithms, Compression, Pattern matching, Run-length encoding}
}
Document
DOI: 10.4230/LIPIcs.STACS.2018.22
Upper and Lower Bounds for Dynamic Data Structures on Strings

Authors: Raphaël Clifford, Allan Grønlund, Kasper Green Larsen, and Tatiana Starikovskaya

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract
We consider a range of simply stated dynamic data structure problems on strings. An update changes one symbol in the input and a query asks us to compute some function of the pattern of length m and a substring of a longer text. We give both conditional and unconditional lower bounds for variants of exact matching with wildcards, inner product, and Hamming distance computation via a sequence of reductions. As an example, we show that there does not exist an O(m^{1/2-epsilon}) time algorithm for a large range of these problems unless the online Boolean matrix-vector multiplication conjecture is false. We also provide nearly matching upper bounds for most of the problems we consider.
Cite as

Raphaël Clifford, Allan Grønlund, Kasper Green Larsen, and Tatiana Starikovskaya. Upper and Lower Bounds for Dynamic Data Structures on Strings. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 22:1-22:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{clifford_et_al:LIPIcs.STACS.2018.22,
  author =	{Clifford, Rapha\"{e}l and Gr{\o}nlund, Allan and Larsen, Kasper Green and Starikovskaya, Tatiana},
  title =	{{Upper and Lower Bounds for Dynamic Data Structures on Strings}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{22:1--22:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.22},
  URN =		{urn:nbn:de:0030-drops-85088},
  doi =		{10.4230/LIPIcs.STACS.2018.22},
  annote =	{Keywords: exact pattern matching with wildcards, hamming distance, inner product, conditional lower bounds}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.20
Approximate Hamming Distance in a Stream

Authors: Raphaël Clifford and Tatiana Starikovskaya

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
We consider the problem of computing a (1+epsilon)-approximation of the Hamming distance between a pattern of length n and successive substrings of a stream. We first look at the one-way randomised communication complexity of this problem. We show the following: - If Alice and Bob both share the pattern and Alice has the first half of the stream and Bob the second half, then there is an O(epsilon^{-4}*log^2(n)) bit randomised one-way communication protocol. - If Alice has the pattern, Bob the first half of the stream and Charlie the second half, then there is an O(epsilon^{-2}*sqrt(n)*log(n)) bit randomised one-way communication protocol. We then go on to develop small space streaming algorithms for (1 + epsilon)-approximate Hamming distance which give worst case running time guarantees per arriving symbol. - For binary input alphabets there is an O(epsilon^{-3}*sqrt(n)*log^2(n)) space and O(epsilon^{-2}*log(n)) time streaming (1 + epsilon)-approximate Hamming distance algorithm. - For general input alphabets there is an O(epsilon^{-5}*sqrt(n)*log^4(n)) space and O(epsilon^{-4}*log^3(n)) time streaming (1 + epsilon)-approximate Hamming distance algorithm.
Cite as

Raphaël Clifford and Tatiana Starikovskaya. Approximate Hamming Distance in a Stream. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 20:1-20:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{clifford_et_al:LIPIcs.ICALP.2016.20,
  author =	{Clifford, Rapha\"{e}l and Starikovskaya, Tatiana},
  title =	{{Approximate Hamming Distance in a Stream}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{20:1--20:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.20},
  URN =		{urn:nbn:de:0030-drops-62992},
  doi =		{10.4230/LIPIcs.ICALP.2016.20},
  annote =	{Keywords: Hamming distance, communication complexity, data stream model}
}
Document
DOI: 10.4230/LIPIcs.ESA.2016.31
Cell-Probe Lower Bounds for Bit Stream Computation

Authors: Raphaël Clifford, Markus Jalsenius, and Benjamin Sach

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract
We revisit the complexity of online computation in the cell probe model. We consider a class of problems where we are first given a fixed pattern F of n symbols and then one symbol arrives at a time in a stream. After each symbol has arrived we must output some function of F and the n-length suffix of the arriving stream. Cell probe bounds of Omega(delta lg n/w) have previously been shown for both convolution and Hamming distance in this setting, where delta is the size of a symbol in bits and w in Omega(lg n) is the cell size in bits. However, when delta is a constant, as it is in many natural situations, the existing approaches no longer give us non-trivial bounds. We introduce a lop-sided information transfer proof technique which enables us to prove meaningful lower bounds even for constant size input alphabets. Our new framework is capable of proving amortised cell probe lower bounds of Omega(lg^2 n/(w lg lg n)) time per arriving bit. We demonstrate this technique by showing a new lower bound for a problem known as pattern matching with address errors or the L_2-rearrangement distance problem. This gives the first non-trivial cell probe lower bound for any online problem on bit streams that still holds when the cell size is large.
Cite as

Raphaël Clifford, Markus Jalsenius, and Benjamin Sach. Cell-Probe Lower Bounds for Bit Stream Computation. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 31:1-31:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{clifford_et_al:LIPIcs.ESA.2016.31,
  author =	{Clifford, Rapha\"{e}l and Jalsenius, Markus and Sach, Benjamin},
  title =	{{Cell-Probe Lower Bounds for Bit Stream Computation}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{31:1--31:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.31},
  URN =		{urn:nbn:de:0030-drops-63827},
  doi =		{10.4230/LIPIcs.ESA.2016.31},
  annote =	{Keywords: Cell-probe lower bounds, algorithms, data streaming}
}
Document
DOI: 10.4230/DagSemProc.09281.5
Pattern matching with don't cares and few errors

Authors: Raphael Clifford, Klim Efremo, Ely Porat, and Amir Rotschild

Published in: Dagstuhl Seminar Proceedings, Volume 9281, Search Methodologies (2009)

Abstract
We present solutions for the k-mismatch pattern matching problem with don't cares. Given a text t of length n and a pattern p of length m with don't care symbols and a bound k, our algorithms find all the places that the pattern matches the text with at most k mismatches. We first give an \Theta(n(k + logmlog k) log n) time randomised algorithm which finds the correct answer with high probability. We then present a new deter- ministic \Theta(nk^2 log^m)time solution that uses tools originally developed for group testing. Taking our derandomisation approach further we de- velop an approach based on k-selectors that runs in \Theta(nk polylogm) time. Further, in each case the location of the mismatches at each alignment is also given at no extra cost.
Cite as

Raphael Clifford, Klim Efremo, Ely Porat, and Amir Rotschild. Pattern matching with don't cares and few errors. In Search Methodologies. Dagstuhl Seminar Proceedings, Volume 9281, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{clifford_et_al:DagSemProc.09281.5,
  author =	{Clifford, Raphael and Efremo, Klim and Porat, Ely and Rotschild, Amir},
  title =	{{Pattern matching with don't cares and few errors}},
  booktitle =	{Search Methodologies},
  pages =	{1--19},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9281},
  editor =	{Rudolf Ahlswede and Ferdinando Cicalese and Ugo Vaccaro},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09281.5},
  URN =		{urn:nbn:de:0030-drops-22442},
  doi =		{10.4230/DagSemProc.09281.5},
  annote =	{Keywords: Prime Numbers, Group Testing, Streaming, Pattern Matching}
}

Clifford, Raphaël

Document
DOI: 10.4230/LIPIcs.CPM.2022.18
The Dynamic k-Mismatch Problem

Authors: Raphaël Clifford, Paweł Gawrychowski, Tomasz Kociumaka, Daniel P. Martin, and Przemysław Uznański

Published in: LIPIcs, Volume 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)

Abstract
The text-to-pattern Hamming distances problem asks to compute the Hamming distances between a given pattern of length m and all length-m substrings of a given text of length n ≥ m. We focus on the well-studied k-mismatch version of the problem, where a distance needs to be returned only if it does not exceed a threshold k. Moreover, we assume n ≤ 2m (in general, one can partition the text into overlapping blocks). In this work, we develop data structures for the dynamic version of the k-mismatch problem supporting two operations: An update performs a single-letter substitution in the pattern or the text, whereas a query, given an index i, returns the Hamming distance between the pattern and the text substring starting at position i, or reports that the distance exceeds k. First, we describe a simple data structure with 𝒪̃(1) update time and 𝒪̃(k) query time. Through considerably more sophisticated techniques, we show that 𝒪̃(k) update time and 𝒪̃(1) query time is also achievable. These two solutions likely provide an essentially optimal trade-off for the dynamic k-mismatch problem with m^{Ω(1)} ≤ k ≤ √m: we prove that, in that case, conditioned on the 3SUM conjecture, one cannot simultaneously achieve k^{1-Ω(1)} time for all operations (updates and queries) after n^{𝒪(1)}-time initialization. For k ≥ √m, the same lower bound excludes achieving m^{1/2-Ω(1)} time per operation. This is known to be essentially tight for constant-sized alphabets: already Clifford et al. (STACS 2018) achieved 𝒪̃(√m) time per operation in that case, but their solution for large alphabets costs 𝒪̃(m^{3/4}) time per operation. We improve and extend the latter result by developing a trade-off algorithm that, given a parameter 1 ≤ x ≤ k, achieves update time 𝒪̃(m/k +√{mk/x}) and query time 𝒪̃(x). In particular, for k ≥ √m, an appropriate choice of x yields 𝒪̃(∛{mk}) time per operation, which is 𝒪̃(m^{2/3}) when only the trivial threshold k = m is provided.
Cite as

Raphaël Clifford, Paweł Gawrychowski, Tomasz Kociumaka, Daniel P. Martin, and Przemysław Uznański. The Dynamic k-Mismatch Problem. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 18:1-18:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{clifford_et_al:LIPIcs.CPM.2022.18,
  author =	{Clifford, Rapha\"{e}l and Gawrychowski, Pawe{\l} and Kociumaka, Tomasz and Martin, Daniel P. and Uzna\'{n}ski, Przemys{\l}aw},
  title =	{{The Dynamic k-Mismatch Problem}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{18:1--18:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-234-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{223},
  editor =	{Bannai, Hideo and Holub, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.18},
  URN =		{urn:nbn:de:0030-drops-161454},
  doi =		{10.4230/LIPIcs.CPM.2022.18},
  annote =	{Keywords: Pattern matching, Hamming distance, dynamic algorithms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.66
RLE Edit Distance in Near Optimal Time

Authors: Raphaël Clifford, Paweł Gawrychowski, Tomasz Kociumaka, Daniel P. Martin, and Przemysław Uznański

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
We show that the edit distance between two run-length encoded strings of compressed lengths m and n respectively, can be computed in O(mn log(mn)) time. This improves the previous record by a factor of O(n/log(mn)). The running time of our algorithm is within subpolynomial factors of being optimal, subject to the standard SETH-hardness assumption. This effectively closes a line of algorithmic research first started in 1993.
Cite as

Raphaël Clifford, Paweł Gawrychowski, Tomasz Kociumaka, Daniel P. Martin, and Przemysław Uznański. RLE Edit Distance in Near Optimal Time. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 66:1-66:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{clifford_et_al:LIPIcs.MFCS.2019.66,
  author =	{Clifford, Rapha\"{e}l and Gawrychowski, Pawe{\l} and Kociumaka, Tomasz and Martin, Daniel P. and Uzna\'{n}ski, Przemys{\l}aw},
  title =	{{RLE Edit Distance in Near Optimal Time}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{66:1--66:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.66},
  URN =		{urn:nbn:de:0030-drops-110109},
  doi =		{10.4230/LIPIcs.MFCS.2019.66},
  annote =	{Keywords: String algorithms, Compression, Pattern matching, Run-length encoding}
}
Document
DOI: 10.4230/LIPIcs.STACS.2018.22
Upper and Lower Bounds for Dynamic Data Structures on Strings

Authors: Raphaël Clifford, Allan Grønlund, Kasper Green Larsen, and Tatiana Starikovskaya

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract
We consider a range of simply stated dynamic data structure problems on strings. An update changes one symbol in the input and a query asks us to compute some function of the pattern of length m and a substring of a longer text. We give both conditional and unconditional lower bounds for variants of exact matching with wildcards, inner product, and Hamming distance computation via a sequence of reductions. As an example, we show that there does not exist an O(m^{1/2-epsilon}) time algorithm for a large range of these problems unless the online Boolean matrix-vector multiplication conjecture is false. We also provide nearly matching upper bounds for most of the problems we consider.
Cite as

Raphaël Clifford, Allan Grønlund, Kasper Green Larsen, and Tatiana Starikovskaya. Upper and Lower Bounds for Dynamic Data Structures on Strings. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 22:1-22:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{clifford_et_al:LIPIcs.STACS.2018.22,
  author =	{Clifford, Rapha\"{e}l and Gr{\o}nlund, Allan and Larsen, Kasper Green and Starikovskaya, Tatiana},
  title =	{{Upper and Lower Bounds for Dynamic Data Structures on Strings}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{22:1--22:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.22},
  URN =		{urn:nbn:de:0030-drops-85088},
  doi =		{10.4230/LIPIcs.STACS.2018.22},
  annote =	{Keywords: exact pattern matching with wildcards, hamming distance, inner product, conditional lower bounds}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.20
Approximate Hamming Distance in a Stream

Authors: Raphaël Clifford and Tatiana Starikovskaya

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
We consider the problem of computing a (1+epsilon)-approximation of the Hamming distance between a pattern of length n and successive substrings of a stream. We first look at the one-way randomised communication complexity of this problem. We show the following: - If Alice and Bob both share the pattern and Alice has the first half of the stream and Bob the second half, then there is an O(epsilon^{-4}*log^2(n)) bit randomised one-way communication protocol. - If Alice has the pattern, Bob the first half of the stream and Charlie the second half, then there is an O(epsilon^{-2}*sqrt(n)*log(n)) bit randomised one-way communication protocol. We then go on to develop small space streaming algorithms for (1 + epsilon)-approximate Hamming distance which give worst case running time guarantees per arriving symbol. - For binary input alphabets there is an O(epsilon^{-3}*sqrt(n)*log^2(n)) space and O(epsilon^{-2}*log(n)) time streaming (1 + epsilon)-approximate Hamming distance algorithm. - For general input alphabets there is an O(epsilon^{-5}*sqrt(n)*log^4(n)) space and O(epsilon^{-4}*log^3(n)) time streaming (1 + epsilon)-approximate Hamming distance algorithm.
Cite as

Raphaël Clifford and Tatiana Starikovskaya. Approximate Hamming Distance in a Stream. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 20:1-20:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{clifford_et_al:LIPIcs.ICALP.2016.20,
  author =	{Clifford, Rapha\"{e}l and Starikovskaya, Tatiana},
  title =	{{Approximate Hamming Distance in a Stream}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{20:1--20:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.20},
  URN =		{urn:nbn:de:0030-drops-62992},
  doi =		{10.4230/LIPIcs.ICALP.2016.20},
  annote =	{Keywords: Hamming distance, communication complexity, data stream model}
}
Document
DOI: 10.4230/LIPIcs.ESA.2016.31
Cell-Probe Lower Bounds for Bit Stream Computation

Authors: Raphaël Clifford, Markus Jalsenius, and Benjamin Sach

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract
We revisit the complexity of online computation in the cell probe model. We consider a class of problems where we are first given a fixed pattern F of n symbols and then one symbol arrives at a time in a stream. After each symbol has arrived we must output some function of F and the n-length suffix of the arriving stream. Cell probe bounds of Omega(delta lg n/w) have previously been shown for both convolution and Hamming distance in this setting, where delta is the size of a symbol in bits and w in Omega(lg n) is the cell size in bits. However, when delta is a constant, as it is in many natural situations, the existing approaches no longer give us non-trivial bounds. We introduce a lop-sided information transfer proof technique which enables us to prove meaningful lower bounds even for constant size input alphabets. Our new framework is capable of proving amortised cell probe lower bounds of Omega(lg^2 n/(w lg lg n)) time per arriving bit. We demonstrate this technique by showing a new lower bound for a problem known as pattern matching with address errors or the L_2-rearrangement distance problem. This gives the first non-trivial cell probe lower bound for any online problem on bit streams that still holds when the cell size is large.
Cite as

Raphaël Clifford, Markus Jalsenius, and Benjamin Sach. Cell-Probe Lower Bounds for Bit Stream Computation. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 31:1-31:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{clifford_et_al:LIPIcs.ESA.2016.31,
  author =	{Clifford, Rapha\"{e}l and Jalsenius, Markus and Sach, Benjamin},
  title =	{{Cell-Probe Lower Bounds for Bit Stream Computation}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{31:1--31:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.31},
  URN =		{urn:nbn:de:0030-drops-63827},
  doi =		{10.4230/LIPIcs.ESA.2016.31},
  annote =	{Keywords: Cell-probe lower bounds, algorithms, data streaming}
}
Document
DOI: 10.4230/DagSemProc.09281.5
Pattern matching with don't cares and few errors

Authors: Raphael Clifford, Klim Efremo, Ely Porat, and Amir Rotschild

Published in: Dagstuhl Seminar Proceedings, Volume 9281, Search Methodologies (2009)

Abstract
We present solutions for the k-mismatch pattern matching problem with don't cares. Given a text t of length n and a pattern p of length m with don't care symbols and a bound k, our algorithms find all the places that the pattern matches the text with at most k mismatches. We first give an \Theta(n(k + logmlog k) log n) time randomised algorithm which finds the correct answer with high probability. We then present a new deter- ministic \Theta(nk^2 log^m)time solution that uses tools originally developed for group testing. Taking our derandomisation approach further we de- velop an approach based on k-selectors that runs in \Theta(nk polylogm) time. Further, in each case the location of the mismatches at each alignment is also given at no extra cost.
Cite as

Raphael Clifford, Klim Efremo, Ely Porat, and Amir Rotschild. Pattern matching with don't cares and few errors. In Search Methodologies. Dagstuhl Seminar Proceedings, Volume 9281, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{clifford_et_al:DagSemProc.09281.5,
  author =	{Clifford, Raphael and Efremo, Klim and Porat, Ely and Rotschild, Amir},
  title =	{{Pattern matching with don't cares and few errors}},
  booktitle =	{Search Methodologies},
  pages =	{1--19},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9281},
  editor =	{Rudolf Ahlswede and Ferdinando Cicalese and Ugo Vaccaro},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09281.5},
  URN =		{urn:nbn:de:0030-drops-22442},
  doi =		{10.4230/DagSemProc.09281.5},
  annote =	{Keywords: Prime Numbers, Group Testing, Streaming, Pattern Matching}
}
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