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Documents authored by Jo, Seungbum

Document
DOI: 10.4230/LIPIcs.ESA.2024.64
A Simple Representation of Tree Covering Utilizing Balanced Parentheses and Efficient Implementation of Average-Case Optimal RMQs

Authors: Kou Hamada, Sankardeep Chakraborty, Seungbum Jo, Takuto Koriyama, Kunihiko Sadakane, and Srinivasa Rao Satti

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
Tree covering is a technique for decomposing a tree into smaller sized trees with desirable properties, and has been employed in various succinct data structures. However, significant hurdles stand in the way of a practical implementation of tree covering: a lot of pointers are used to maintain the tree-covering hierarchy and many indices for tree navigational queries consume theoretically negligible yet practically vast space. To tackle these problems, we propose a simple representation of tree covering using a balanced-parenthesis representation. The key to the proposal is the observation that every micro tree splits into at most two intervals on the BP representation. Utilizing the representation, we propose several data structures that represent a tree and its tree cover, which consequently allow micro tree compression with arbitrary coding and efficient tree navigational queries. We also applied our data structure to average-case optimal RMQ by Munro et al. [ESA 2021] and implemented the RMQ data structure. Our RMQ data structures spend less than 2n bits and process queries in a practical time on several settings of the performance evaluation, reducing the gap between theoretical space complexity and actual space consumption. For example, our implementation consumes 1.822n bits and processes queries in 5µs on average for random queries and in 13µs on average for the worst query widths. We also implement tree navigational operations while using the same amount of space as the RMQ data structures. We believe the representation can be widely utilized for designing practically memory-efficient data structures based on tree covering.
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Kou Hamada, Sankardeep Chakraborty, Seungbum Jo, Takuto Koriyama, Kunihiko Sadakane, and Srinivasa Rao Satti. A Simple Representation of Tree Covering Utilizing Balanced Parentheses and Efficient Implementation of Average-Case Optimal RMQs. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 64:1-64:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hamada_et_al:LIPIcs.ESA.2024.64,
  author =	{Hamada, Kou and Chakraborty, Sankardeep and Jo, Seungbum and Koriyama, Takuto and Sadakane, Kunihiko and Satti, Srinivasa Rao},
  title =	{{A Simple Representation of Tree Covering Utilizing Balanced Parentheses and Efficient Implementation of Average-Case Optimal RMQs}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{64:1--64:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.64},
  URN =		{urn:nbn:de:0030-drops-211359},
  doi =		{10.4230/LIPIcs.ESA.2024.64},
  annote =	{Keywords: Hypersuccinct trees, Succinct data structures, Range minimum queries, Binary trees}
}
Document
DOI: 10.4230/LIPIcs.SEA.2021.10
Practical Implementation of Encoding Range Top-2 Queries

Authors: Seungbum Jo, Wooyoung Park, and Srinivasa Rao Satti

Published in: LIPIcs, Volume 190, 19th International Symposium on Experimental Algorithms (SEA 2021)

Abstract
We design a practical variant of an encoding for range Top-2 queries (RT2Q), and evaluate its performance. Given an array A[1,n] of n elements from a total order, the range Top-2 encoding problem is to construct a data structure that can answer RT2Q queries, which return the positions of the first and the second largest elements within a given query range of A, without accessing the array A at query time. Davoodi et al. [Phil. Trans. Royal Soc. A, 2016] proposed a (3.272n + o(n))-bit encoding, which answers RT2Q queries in O(1) time, while Gawrychowski and Nicholson [ICALP, 2015] gave an optimal (2.755n + (n))-bit encoding which doesn't support efficient queries. In this paper, we propose the first practical implementation of the encoding data structure for answering RT2Q. Our implementation is based on an alternative representation of Davoodi et al.’s data structure. The experimental results show that our implementation is efficient in practice, and gives improved time-space trade-offs compared to the indexing data structures (which keep the original array A as part of the data structure) for range maximum queries.
Cite as

Seungbum Jo, Wooyoung Park, and Srinivasa Rao Satti. Practical Implementation of Encoding Range Top-2 Queries. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{jo_et_al:LIPIcs.SEA.2021.10,
  author =	{Jo, Seungbum and Park, Wooyoung and Satti, Srinivasa Rao},
  title =	{{Practical Implementation of Encoding Range Top-2 Queries}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{10:1--10:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-185-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{190},
  editor =	{Coudert, David and Natale, Emanuele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.10},
  URN =		{urn:nbn:de:0030-drops-137827},
  doi =		{10.4230/LIPIcs.SEA.2021.10},
  annote =	{Keywords: Range top-2 query, Range minimum query, Cartesian tree, Succinct encoding}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.54
Approximate Query Processing over Static Sets and Sliding Windows

Authors: Ran Ben Basat, Seungbum Jo, Srinivasa Rao Satti, and Shubham Ugare

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
Indexing of static and dynamic sets is fundamental to a large set of applications such as information retrieval and caching. Denoting the characteristic vector of the set by B, we consider the problem of encoding sets and multisets to support approximate versions of the operations rank(i) (i.e., computing sum_{j <= i} B[j]) and select(i) (i.e., finding min{p|rank(p) >= i}) queries. We study multiple types of approximations (allowing an error in the query or the result) and present lower bounds and succinct data structures for several variants of the problem. We also extend our model to sliding windows, in which we process a stream of elements and compute suffix sums. This is a generalization of the window summation problem that allows the user to specify the window size at query time. Here, we provide an algorithm that supports updates and queries in constant time while requiring just (1+o(1)) factor more space than the fixed-window summation algorithms.
Cite as

Ran Ben Basat, Seungbum Jo, Srinivasa Rao Satti, and Shubham Ugare. Approximate Query Processing over Static Sets and Sliding Windows. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 54:1-54:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{benbasat_et_al:LIPIcs.ISAAC.2018.54,
  author =	{Ben Basat, Ran and Jo, Seungbum and Satti, Srinivasa Rao and Ugare, Shubham},
  title =	{{Approximate Query Processing over Static Sets and Sliding Windows}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{54:1--54:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.54},
  URN =		{urn:nbn:de:0030-drops-100027},
  doi =		{10.4230/LIPIcs.ISAAC.2018.54},
  annote =	{Keywords: Streaming, Algorithms, Sliding window, Lower bounds}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.69
Encoding Two-Dimensional Range Top-k Queries Revisited

Authors: Seungbum Jo and Srinivasa Rao Satti

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
We consider the problem of encoding two-dimensional arrays, whose elements come from a total order, for answering Top-k queries. The aim is to obtain encodings that use space close to the information-theoretic lower bound, which can be constructed efficiently. For 2 x n arrays, we first give upper and lower bounds on space for answering sorted and unsorted 3-sided Top-k queries. For m x n arrays, with m <=n and k <=mn, we obtain (m lg{(k+1)n choose n}+4nm(m-1)+o(n))-bit encoding for answering sorted 4-sided Top-k queries. This improves the min{(O(mn lg{n}),m^2 lg{(k+1)n choose n} + m lg{m}+o(n))}-bit encoding of Jo et al. [CPM, 2016] when m = o(lg{n}). This is a consequence of a new encoding that encodes a 2 x n array to support sorted 4-sided Top-k queries on it using an additional 4n bits, in addition to the encodings to support the Top-k queries on individual rows. This new encoding is a non-trivial generalization of the encoding of Jo et al. [CPM, 2016] that supports sorted 4-sided Top-2 queries on it using an additional 3n bits. We also give almost optimal space encodings for 3-sided Top-k queries, and show lower bounds on encodings for 3-sided and 4-sided Top-k queries.
Cite as

Seungbum Jo and Srinivasa Rao Satti. Encoding Two-Dimensional Range Top-k Queries Revisited. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 69:1-69:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{jo_et_al:LIPIcs.ISAAC.2018.69,
  author =	{Jo, Seungbum and Satti, Srinivasa Rao},
  title =	{{Encoding Two-Dimensional Range Top-k Queries Revisited}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{69:1--69:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.69},
  URN =		{urn:nbn:de:0030-drops-100179},
  doi =		{10.4230/LIPIcs.ISAAC.2018.69},
  annote =	{Keywords: Encoding model, top-k query, range minimum query}
}
Document
DOI: 10.4230/LIPIcs.CPM.2016.3
Encoding Two-Dimensional Range Top-k Queries

Authors: Seungbum Jo, Rahul Lingala, and Srinivasa Rao Satti

Published in: LIPIcs, Volume 54, 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)

Abstract
We consider various encodings that support range top-k queries on a two-dimensional array containing elements from a total order. For an m x n array, we first propose an almost optimal encoding for answering one-sided top-k queries, whose query range is restricted to [1 ... m][1 .. a], for 1 <= a <= n. Next, we propose an encoding for the general top-k queries that takes m^2 * lg(binom((k+1)n)(n)) + m * lg(m) + o(n) bits. This generalizes the one-dimensional top-k encoding of Gawrychowski and Nicholson [ICALP, 2015]. Finally, for a 2 x n array, we obtain a 2 lg(binom(3n)(n)) + 3n + o(n)-bit encoding for answering top-2 queries.
Cite as

Seungbum Jo, Rahul Lingala, and Srinivasa Rao Satti. Encoding Two-Dimensional Range Top-k Queries. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 3:1-3:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{jo_et_al:LIPIcs.CPM.2016.3,
  author =	{Jo, Seungbum and Lingala, Rahul and Satti, Srinivasa Rao},
  title =	{{Encoding Two-Dimensional Range Top-k Queries}},
  booktitle =	{27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
  pages =	{3:1--3:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-012-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{54},
  editor =	{Grossi, Roberto and Lewenstein, Moshe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2016.3},
  URN =		{urn:nbn:de:0030-drops-60704},
  doi =		{10.4230/LIPIcs.CPM.2016.3},
  annote =	{Keywords: Encoding model, top-k query, range minimum query}
}
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