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Documents authored by Lu, Shangqi

Document
DOI: 10.4230/LIPIcs.ICDT.2023.6
Space-Query Tradeoffs in Range Subgraph Counting and Listing

Authors: Shiyuan Deng, Shangqi Lu, and Yufei Tao

Published in: LIPIcs, Volume 255, 26th International Conference on Database Theory (ICDT 2023)

Abstract
This paper initializes the study of range subgraph counting and range subgraph listing, both of which are motivated by the significant demands in practice to perform graph analytics on subgraphs pertinent to only selected, as opposed to all, vertices. In the first problem, there is an undirected graph G where each vertex carries a real-valued attribute. Given an interval q and a pattern Q, a query counts the number of occurrences of Q in the subgraph of G induced by the vertices whose attributes fall in q. The second problem has the same setup except that a query needs to enumerate (rather than count) those occurrences with a small delay. In both problems, our goal is to understand the tradeoff between space usage and query cost, or more specifically: (i) given a target on query efficiency, how much pre-computed information about G must we store? (ii) Or conversely, given a budget on space usage, what is the best query time we can hope for? We establish a suite of upper- and lower-bound results on such tradeoffs for various query patterns.
Cite as

Shiyuan Deng, Shangqi Lu, and Yufei Tao. Space-Query Tradeoffs in Range Subgraph Counting and Listing. In 26th International Conference on Database Theory (ICDT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 255, pp. 6:1-6:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{deng_et_al:LIPIcs.ICDT.2023.6,
  author =	{Deng, Shiyuan and Lu, Shangqi and Tao, Yufei},
  title =	{{Space-Query Tradeoffs in Range Subgraph Counting and Listing}},
  booktitle =	{26th International Conference on Database Theory (ICDT 2023)},
  pages =	{6:1--6:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-270-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{255},
  editor =	{Geerts, Floris and Vandevoort, Brecht},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2023.6},
  URN =		{urn:nbn:de:0030-drops-177484},
  doi =		{10.4230/LIPIcs.ICDT.2023.6},
  annote =	{Keywords: Subgraph Pattern Counting, Subgraph Pattern Listing, Conjunctive Queries}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.57
Range Updates and Range Sum Queries on Multidimensional Points with Monoid Weights

Authors: Shangqi Lu and Yufei Tao

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
Let P be a set of n points in ℝ^d where each point p ∈ P carries a weight drawn from a commutative monoid (ℳ, +, 0). Given a d-rectangle r_upd (i.e., an orthogonal rectangle in ℝ^d) and a value Δ ∈ ℳ, a range update adds Δ to the weight of every point p ∈ P∩ r_upd; given a d-rectangle r_qry, a range sum query returns the total weight of the points in P ∩ r_qry. The goal is to store P in a structure to support updates and queries with attractive performance guarantees. We describe a structure of Õ(n) space that handles an update in Õ(T_upd) time and a query in Õ(T_qry) time for arbitrary functions T_upd(n) and T_qry(n) satisfying T_upd ⋅ T_qry = n. The result holds for any fixed dimensionality d ≥ 2. Our query-update tradeoff is tight up to a polylog factor subject to the OMv-conjecture.
Cite as

Shangqi Lu and Yufei Tao. Range Updates and Range Sum Queries on Multidimensional Points with Monoid Weights. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 57:1-57:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lu_et_al:LIPIcs.ISAAC.2022.57,
  author =	{Lu, Shangqi and Tao, Yufei},
  title =	{{Range Updates and Range Sum Queries on Multidimensional Points with Monoid Weights}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{57:1--57:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.57},
  URN =		{urn:nbn:de:0030-drops-173427},
  doi =		{10.4230/LIPIcs.ISAAC.2022.57},
  annote =	{Keywords: Range Updates, Range Sum Queries, Data Structures, Lower Bounds}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2021.6
Towards Optimal Dynamic Indexes for Approximate (and Exact) Triangle Counting

Authors: Shangqi Lu and Yufei Tao

Published in: LIPIcs, Volume 186, 24th International Conference on Database Theory (ICDT 2021)

Abstract
In ICDT'19, Kara, Ngo, Nikolic, Olteanu, and Zhang gave a structure which maintains the number T of triangles in an undirected graph G = (V, E) along with the edge insertions/deletions in G. Using O(m) space (m = |E|), their structure supports an update in O(√m log m) amortized time which is optimal (up to polylog factors) subject to the OMv-conjecture (Henzinger, Krinninger, Nanongkai, and Saranurak, STOC'15). Aiming to improve the update efficiency, we study: - the optimal tradeoff between update time and approximation quality. We require a structure to provide the (ε, Γ)-guarantee: when queried, it should return an estimate t of T that has relative error at most ε if T ≥ Γ, or an absolute error at most ε ⋅ Γ, otherwise. We prove that, under any ε ≤ 0.49 and subject to the OMv-conjecture, no structure can guarantee O(m^{0.5-δ}/Γ) expected amortized update time and O(m^{2/3-δ}) query time simultaneously for any constant δ > 0; this is true for Γ = m^c of any constant c in [0, 1/2). We match the lower bound with a structure that ensures Õ((1/ε)³ ⋅ √m/Γ) amortized update time with high probability, and O(1) query time. - (for exact counting) how to achieve arboricity-sensitive update time. For any 1 ≤ Γ ≤ √m, we describe a structure of O(min{α m + m log m, (m/Γ)²}) space that maintains T precisely, and supports an update in Õ(min{α + Γ, √m}) amortized time, where α is the largest arboricity of G in history (and does not need to be known). Our structure reconstructs the aforementioned ICDT'19 result up to polylog factors by setting Γ = √m, but achieves Õ(m^{0.5-δ}) update time as long as α = O(m^{0.5-δ}).
Cite as

Shangqi Lu and Yufei Tao. Towards Optimal Dynamic Indexes for Approximate (and Exact) Triangle Counting. In 24th International Conference on Database Theory (ICDT 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 186, pp. 6:1-6:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{lu_et_al:LIPIcs.ICDT.2021.6,
  author =	{Lu, Shangqi and Tao, Yufei},
  title =	{{Towards Optimal Dynamic Indexes for Approximate (and Exact) Triangle Counting}},
  booktitle =	{24th International Conference on Database Theory (ICDT 2021)},
  pages =	{6:1--6:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-179-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{186},
  editor =	{Yi, Ke and Wei, Zhewei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2021.6},
  URN =		{urn:nbn:de:0030-drops-137146},
  doi =		{10.4230/LIPIcs.ICDT.2021.6},
  annote =	{Keywords: Triangle Counting, Data Structures, Lower Bounds, Graph Algorithms}
}
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