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Documents authored by Bhattacharya, Sudatta

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.32
Constant Rate Isometric Embeddings of Hamming Metric into Edit Metric

Authors: Sudatta Bhattacharya, Sanjana Dey, Elazar Goldenberg, Mursalin Habib, Bernhard Haeupler, Karthik C. S., and Michal Koucký

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
A function φ: {0,1}^n → {0,1}^N is called an isometric embedding of the n-dimensional Hamming metric space to the N-dimensional edit metric space if, for all x, y ∈ {0,1}ⁿ, the Hamming distance between x and y is equal to the edit distance between φ(x) and φ(y). The rate of such an embedding is defined as the ratio n/N. It is well known in the literature how to construct isometric embeddings with a rate of Ω(1/log n). However, achieving even near-isometric embeddings with a positive constant rate has remained elusive until now. In this paper, we present an isometric embedding with a rate of 1/8 by discovering connections to synchronization strings, which were studied in the context of insertion-deletion codes (Haeupler-Shahrasbi [JACM'21]). At a technical level, we introduce a framework for obtaining high-rate isometric embeddings using a novel object called a misaligner. We speculate that, with sufficient computational resources, our framework could potentially yield isometric embeddings with a rate of 1/5. As an immediate consequence of our constant rate isometric embedding, we improve known conditional lower bounds for the closest pair problem and the discrete 1-center problem in the edit metric and NP-hardness of approximation results for clustering problems and the Steiner tree problem in the edit metric, but now with optimal dependency on the dimension. Furthermore, we obtain optimal lower bounds for the gap edit distance problem in the two-player randomized communication complexity model. We complement our results by showing that no isometric embedding φ:{0,1}^n → {0,1}^N can have rate greater than 15/32 for all positive integers n. En route to proving this upper bound, we uncover fundamental structural properties necessary for every Hamming-to-edit isometric embedding. We also prove similar upper and lower bounds for embeddings over larger alphabets. Finally, we consider embeddings φ:Σ_in^n → Σ_out^N between different input and output alphabets, where the rate is given by (n log|Σ_in|)/(Nlog|Σ_out|). In this setting, we show that the rate can be made arbitrarily close to 1.
Cite as

Sudatta Bhattacharya, Sanjana Dey, Elazar Goldenberg, Mursalin Habib, Bernhard Haeupler, Karthik C. S., and Michal Koucký. Constant Rate Isometric Embeddings of Hamming Metric into Edit Metric. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 32:1-32:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bhattacharya_et_al:LIPIcs.ICALP.2026.32,
  author =	{Bhattacharya, Sudatta and Dey, Sanjana and Goldenberg, Elazar and Habib, Mursalin and Haeupler, Bernhard and Karthik C. S. and Kouck\'{y}, Michal},
  title =	{{Constant Rate Isometric Embeddings of Hamming Metric into Edit Metric}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{32:1--32:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.32},
  URN =		{urn:nbn:de:0030-drops-264215},
  doi =		{10.4230/LIPIcs.ICALP.2026.32},
  annote =	{Keywords: Edit distance, Hamming distance, metric embeddings, synchronization strings, fine-grained complexity}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2024.11
Many Flavors of Edit Distance

Authors: Sudatta Bhattacharya, Sanjana Dey, Elazar Goldenberg, and Michal Koucký

Published in: LIPIcs, Volume 323, 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)

Abstract
Several measures exist for string similarity, including notable ones like the edit distance and the indel distance. The former measures the count of insertions, deletions, and substitutions required to transform one string into another, while the latter specifically quantifies the number of insertions and deletions. Many algorithmic solutions explicitly address one of these measures, and frequently techniques applicable to one can also be adapted to work with the other. In this paper, we investigate whether there exists a standardized approach for applying results from one setting to another. Specifically, we demonstrate the capability to reduce questions regarding string similarity over arbitrary alphabets to equivalent questions over a binary alphabet. Furthermore, we illustrate how to transform questions concerning indel distance into equivalent questions based on edit distance. This complements an earlier result of Tiskin (2007) which addresses the inverse direction.
Cite as

Sudatta Bhattacharya, Sanjana Dey, Elazar Goldenberg, and Michal Koucký. Many Flavors of Edit Distance. In 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bhattacharya_et_al:LIPIcs.FSTTCS.2024.11,
  author =	{Bhattacharya, Sudatta and Dey, Sanjana and Goldenberg, Elazar and Kouck\'{y}, Michal},
  title =	{{Many Flavors of Edit Distance}},
  booktitle =	{44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)},
  pages =	{11:1--11:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-355-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{323},
  editor =	{Barman, Siddharth and Lasota, S{\l}awomir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2024.11},
  URN =		{urn:nbn:de:0030-drops-222004},
  doi =		{10.4230/LIPIcs.FSTTCS.2024.11},
  annote =	{Keywords: Edit distance, Indel distance, Embedding, LCS, Alphabet Reduction}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.22
Streaming k-Edit Approximate Pattern Matching via String Decomposition

Authors: Sudatta Bhattacharya and Michal Koucký

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
In this paper we give an algorithm for streaming k-edit approximate pattern matching which uses space Õ(k²) and time Õ(k²) per arriving symbol. This improves substantially on the recent algorithm of Kociumaka, Porat and Starikovskaya [Kociumaka et al., 2022] which uses space Õ(k⁵) and time Õ(k⁸) per arriving symbol. In the k-edit approximate pattern matching problem we get a pattern P and text T and we want to identify all substrings of the text T that are at edit distance at most k from P. In the streaming version of this problem both the pattern and the text arrive in a streaming fashion symbol by symbol and after each symbol of the text we need to report whether there is a current suffix of the text with edit distance at most k from P. We measure the total space needed by the algorithm and time needed per arriving symbol.
Cite as

Sudatta Bhattacharya and Michal Koucký. Streaming k-Edit Approximate Pattern Matching via String Decomposition. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 22:1-22:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bhattacharya_et_al:LIPIcs.ICALP.2023.22,
  author =	{Bhattacharya, Sudatta and Kouck\'{y}, Michal},
  title =	{{Streaming k-Edit Approximate Pattern Matching via String Decomposition}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{22:1--22:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.22},
  URN =		{urn:nbn:de:0030-drops-180741},
  doi =		{10.4230/LIPIcs.ICALP.2023.22},
  annote =	{Keywords: Approximate pattern matching, edit distance, streaming algorithms}
}
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