4 Search Results for "Wang, Zhengyu"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.75
Tight Bounds for Heavy-Hitters and Moment Estimation in the Sliding Window Model

Authors: Shiyuan Feng, William Swartworth, and David Woodruff

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We consider the heavy-hitters and F_p moment estimation problems in the sliding window model. For F_p moment estimation with 1 < p ≤ 2, we show that it is possible to give a (1± ε) multiplicative approximation to the F_p moment with 2/3 probability on any given window of size n using Õ(1/(ε^p)log² n + 1/(ε²)log n) bits of space. We complement this result with a lower bound showing that our algorithm gives tight bounds up to factors of log log n and log1/(ε). As a consequence of our F₂ moment estimation algorithm, we show that the heavy-hitters problem can be solved on an arbitrary window using O(1/(ε²)log² n) space which is tight.
Cite as

Shiyuan Feng, William Swartworth, and David Woodruff. Tight Bounds for Heavy-Hitters and Moment Estimation in the Sliding Window Model. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 75:1-75:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{feng_et_al:LIPIcs.ICALP.2025.75,
  author =	{Feng, Shiyuan and Swartworth, William and Woodruff, David},
  title =	{{Tight Bounds for Heavy-Hitters and Moment Estimation in the Sliding Window Model}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{75:1--75:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l 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.2025.75},
  URN =		{urn:nbn:de:0030-drops-234524},
  doi =		{10.4230/LIPIcs.ICALP.2025.75},
  annote =	{Keywords: sketching, streaming, heavy hitters, sliding window, moment estimation}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2025.7
O(1)-Round MPC Algorithms for Multi-Dimensional Grid Graph Connectivity, Euclidean MST and DBSCAN

Authors: Junhao Gan, Anthony Wirth, and Zhuo Zhang

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract
In this paper, we investigate three fundamental problems in the Massively Parallel Computation (MPC) model: (i) grid graph connectivity, (ii) approximate Euclidean Minimum Spanning Tree (EMST), and (iii) approximate DBSCAN. Our first result is a O(1)-round Las Vegas (i.e., succeeding with high probability) MPC algorithm for computing the connected components on a d-dimensional c-penetration grid graph ((d,c)-grid graph), where both d and c are positive integer constants. In such a grid graph, each vertex is a point with integer coordinates in ℕ^d, and an edge can only exist between two distinct vertices with 𝓁_∞-norm at most c. To our knowledge, the current best existing result for computing the connected components (CC’s) on (d,c)-grid graphs in the MPC model is to run the state-of-the-art MPC CC algorithms that are designed for general graphs: they achieve O(log log n + log D) [Behnezhad et al., 2019] and O(log log n + log 1/(λ)) [Sepehr Assadi et al., 2019] rounds, respectively, where D is the diameter and λ is the spectral gap of the graph. With our grid graph connectivity technique, our second main result is a O(1)-round Las Vegas MPC algorithm for computing approximate Euclidean MST. The existing state-of-the-art result on this problem is the O(1)-round MPC algorithm proposed by Andoni et al. [Alexandr Andoni et al., 2014], which only guarantees an approximation on the overall weight in expectation. In contrast, our algorithm not only guarantees a deterministic overall weight approximation, but also achieves a deterministic edge-wise weight approximation. The latter property is crucial to many applications, such as finding the Bichromatic Closest Pair and Single-Linkage Clustering. Last, but not least, our third main result is a O(1)-round Las Vegas MPC algorithm for computing an approximate DBSCAN clustering in O(1)-dimensional Euclidean space.
Cite as

Junhao Gan, Anthony Wirth, and Zhuo Zhang. O(1)-Round MPC Algorithms for Multi-Dimensional Grid Graph Connectivity, Euclidean MST and DBSCAN. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gan_et_al:LIPIcs.ICDT.2025.7,
  author =	{Gan, Junhao and Wirth, Anthony and Zhang, Zhuo},
  title =	{{O(1)-Round MPC Algorithms for Multi-Dimensional Grid Graph Connectivity, Euclidean MST and DBSCAN}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{7:1--7:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.7},
  URN =		{urn:nbn:de:0030-drops-229483},
  doi =		{10.4230/LIPIcs.ICDT.2025.7},
  annote =	{Keywords: Massively Parallel Computation, Graph Connectivity, Grid Graphs, Euclidean Minimum Spanning Tree, DBSCAN}
}
Document
DOI: 10.4230/LIPIcs.CCC.2015.412
Non-Commutative Formulas and Frege Lower Bounds: a New Characterization of Propositional Proofs

Authors: Fu Li, Iddo Tzameret, and Zhengyu Wang

Published in: LIPIcs, Volume 33, 30th Conference on Computational Complexity (CCC 2015)

Abstract
Does every Boolean tautology have a short propositional-calculus proof? Here, a propositional-calculus (i.e. Frege) proof is any proof starting from a set of axioms and deriving new Boolean formulas using a fixed set of sound derivation rules. Establishing any super-polynomial size lower bound on Frege proofs (in terms of the size of the formula proved) is a major open problem in proof complexity, and among a handful of fundamental hardness questions in complexity theory by and large. Non-commutative arithmetic formulas, on the other hand, constitute a quite weak computational model, for which exponential-size lower bounds were shown already back in 1991 by Nisan [STOC 1991], using a particularly transparent argument. In this work we show that Frege lower bounds in fact follow from corresponding size lower bounds on non-commutative formulas computing certain polynomials (and that such lower bounds on non-commutative formulas must exist, unless NP=coNP). More precisely, we demonstrate a natural association between tautologies T to non-commutative polynomials p, such that: (*) if T has a polynomial-size Frege proof then p has a polynomial-size non-commutative arithmetic formula; and conversely, when T is a DNF, if p has a polynomial-size non-commutative arithmetic formula over GF(2) then T has a Frege proof of quasi-polynomial size. The argument is a characterization of Frege proofs as non-commutative formulas: we show that the Frege system is (quasi-)polynomially equivalent to a non-commutative Ideal Proof System (IPS), following the recent work of Grochow and Pitassi [FOCS 2014] that introduced a propositional proof system in which proofs are arithmetic circuits, and the work in [Tzameret 2011] that considered adding the commutator as an axiom in algebraic propositional proof systems. This gives a characterization of propositional Frege proofs in terms of (non-commutative) arithmetic formulas that is tighter than (the formula version of IPS) in Grochow and Pitassi [FOCS 2014], in the following sense: (i) The non-commutative IPS is polynomial-time checkable - whereas the original IPS was checkable in probabilistic polynomial-time; and (ii) Frege proofs unconditionally quasi-polynomially simulate the non-commutative IPS - whereas Frege was shown to efficiently simulate IPS only assuming that the decidability of PIT for (commutative) arithmetic formulas by polynomial-size circuits is efficiently provable in Frege.
Cite as

Fu Li, Iddo Tzameret, and Zhengyu Wang. Non-Commutative Formulas and Frege Lower Bounds: a New Characterization of Propositional Proofs. In 30th Conference on Computational Complexity (CCC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 33, pp. 412-432, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{li_et_al:LIPIcs.CCC.2015.412,
  author =	{Li, Fu and Tzameret, Iddo and Wang, Zhengyu},
  title =	{{Non-Commutative Formulas and Frege Lower Bounds: a New Characterization of Propositional Proofs}},
  booktitle =	{30th Conference on Computational Complexity (CCC 2015)},
  pages =	{412--432},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-81-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{33},
  editor =	{Zuckerman, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2015.412},
  URN =		{urn:nbn:de:0030-drops-50585},
  doi =		{10.4230/LIPIcs.CCC.2015.412},
  annote =	{Keywords: Proof complexity, algebraic complexity, arithmetic circuits, Frege, non-commutative formulas}
}
Document
DOI: 10.4230/DagSemProc.05391.9
Verification of Solutions for Almost Linear Complementarity Problems

Authors: Götz Alefeld and Zhengyu Wang

Published in: Dagstuhl Seminar Proceedings, Volume 5391, Algebraic and Numerical Algorithms and Computer-assisted Proofs (2006)

Abstract
We present a computational enclosure method for the solution of a class of nonlinear complementarity problems. The procedure also delivers a proof for the uniqueness of the solution.
Cite as

Götz Alefeld and Zhengyu Wang. Verification of Solutions for Almost Linear Complementarity Problems. In Algebraic and Numerical Algorithms and Computer-assisted Proofs. Dagstuhl Seminar Proceedings, Volume 5391, pp. 1-21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{alefeld_et_al:DagSemProc.05391.9,
  author =	{Alefeld, G\"{o}tz and Wang, Zhengyu},
  title =	{{Verification of Solutions for  Almost Linear  Complementarity Problems}},
  booktitle =	{Algebraic and Numerical Algorithms and Computer-assisted Proofs},
  pages =	{1--21},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{5391},
  editor =	{Bruno Buchberger and Shin'ichi Oishi and Michael Plum and Sigfried M. Rump},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05391.9},
  URN =		{urn:nbn:de:0030-drops-4431},
  doi =		{10.4230/DagSemProc.05391.9},
  annote =	{Keywords: Complementarity problems, verification of solutions}
}
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