Search Results

Documents authored by Yang, Guang

Document
DOI: 10.4230/LIPIcs.ICDT.2025.19
Beyond Logarithmic Bounds: Querying in Constant Expected Time with Learned Indexes

Authors: Luis Alberto Croquevielle, Guang Yang, Liang Liang, Ali Hadian, and Thomas Heinis

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

Abstract
Learned indexes leverage machine learning models to accelerate query answering in databases, showing impressive practical performance. However, theoretical understanding of these methods remains incomplete. Existing research suggests that learned indexes have superior asymptotic complexity compared to their non-learned counterparts, but these findings have been established under restrictive probabilistic assumptions. Specifically, for a sorted array with n elements, it has been shown that learned indexes can find a key in O(log(log n)) expected time using at most linear space, compared with O(log n) for non-learned methods. In this work, we prove O(1) expected time can be achieved with at most linear space, thereby establishing the tightest upper bound so far for the time complexity of an asymptotically optimal learned index. Notably, we use weaker probabilistic assumptions than prior research, meaning our work generalizes previous results. Furthermore, we introduce a new measure of statistical complexity for data. This metric exhibits an information-theoretical interpretation and can be estimated in practice. This characterization provides further theoretical understanding of learned indexes, by helping to explain why some datasets seem to be particularly challenging for these methods.
Cite as

Luis Alberto Croquevielle, Guang Yang, Liang Liang, Ali Hadian, and Thomas Heinis. Beyond Logarithmic Bounds: Querying in Constant Expected Time with Learned Indexes. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 19:1-19:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{croquevielle_et_al:LIPIcs.ICDT.2025.19,
  author =	{Croquevielle, Luis Alberto and Yang, Guang and Liang, Liang and Hadian, Ali and Heinis, Thomas},
  title =	{{Beyond Logarithmic Bounds: Querying in Constant Expected Time with Learned Indexes}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{19:1--19:21},
  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.2025.19},
  URN =		{urn:nbn:de:0030-drops-229603},
  doi =		{10.4230/LIPIcs.ICDT.2025.19},
  annote =	{Keywords: Learned Indexes, Expected Time, Stochastic Processes, R\'{e}nyi Entropy}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.94
Querying a Matrix Through Matrix-Vector Products

Authors: Xiaoming Sun, David P. Woodruff, Guang Yang, and Jialin Zhang

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
We consider algorithms with access to an unknown matrix M in F^{n x d} via matrix-vector products, namely, the algorithm chooses vectors v^1, ..., v^q, and observes Mv^1, ..., Mv^q. Here the v^i can be randomized as well as chosen adaptively as a function of Mv^1, ..., Mv^{i-1}. Motivated by applications of sketching in distributed computation, linear algebra, and streaming models, as well as connections to areas such as communication complexity and property testing, we initiate the study of the number q of queries needed to solve various fundamental problems. We study problems in three broad categories, including linear algebra, statistics problems, and graph problems. For example, we consider the number of queries required to approximate the rank, trace, maximum eigenvalue, and norms of a matrix M; to compute the AND/OR/Parity of each column or row of M, to decide whether there are identical columns or rows in M or whether M is symmetric, diagonal, or unitary; or to compute whether a graph defined by M is connected or triangle-free. We also show separations for algorithms that are allowed to obtain matrix-vector products only by querying vectors on the right, versus algorithms that can query vectors on both the left and the right. We also show separations depending on the underlying field the matrix-vector product occurs in. For graph problems, we show separations depending on the form of the matrix (bipartite adjacency versus signed edge-vertex incidence matrix) to represent the graph. Surprisingly, this fundamental model does not appear to have been studied on its own, and we believe a thorough investigation of problems in this model would be beneficial to a number of different application areas.
Cite as

Xiaoming Sun, David P. Woodruff, Guang Yang, and Jialin Zhang. Querying a Matrix Through Matrix-Vector Products. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 94:1-94:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{sun_et_al:LIPIcs.ICALP.2019.94,
  author =	{Sun, Xiaoming and Woodruff, David P. and Yang, Guang and Zhang, Jialin},
  title =	{{Querying a Matrix Through Matrix-Vector Products}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{94:1--94:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.94},
  URN =		{urn:nbn:de:0030-drops-106709},
  doi =		{10.4230/LIPIcs.ICALP.2019.94},
  annote =	{Keywords: Communication complexity, linear algebra, sketching}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.97
Separating k-Player from t-Player One-Way Communication, with Applications to Data Streams

Authors: David P. Woodruff and Guang Yang

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
In a k-party communication problem, the k players with inputs x_1, x_2, ..., x_k, respectively, want to evaluate a function f(x_1, x_2, ..., x_k) using as little communication as possible. We consider the message-passing model, in which the inputs are partitioned in an arbitrary, possibly worst-case manner, among a smaller number t of players (t<k). The t-player communication cost of computing f can only be smaller than the k-player communication cost, since the t players can trivially simulate the k-player protocol. But how much smaller can it be? We study deterministic and randomized protocols in the one-way model, and provide separations for product input distributions, which are optimal for low error probability protocols. We also provide much stronger separations when the input distribution is non-product. A key application of our results is in proving lower bounds for data stream algorithms. In particular, we give an optimal Omega(epsilon^{-2}log(N) log log(mM)) bits of space lower bound for the fundamental problem of (1 +/-{epsilon})-approximating the number |x |_0 of non-zero entries of an n-dimensional vector x after m updates each of magnitude M, and with success probability >= 2/3, in a strict turnstile stream. Our result matches the best known upper bound when epsilon >= 1/polylog(mM). It also improves on the prior Omega({epsilon}^{-2}log(mM)) lower bound and separates the complexity of approximating L_0 from approximating the p-norm L_p for p bounded away from 0, since the latter has an O(epsilon^{-2}log(mM)) bit upper bound.
Cite as

David P. Woodruff and Guang Yang. Separating k-Player from t-Player One-Way Communication, with Applications to Data Streams. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 97:1-97:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{woodruff_et_al:LIPIcs.ICALP.2019.97,
  author =	{Woodruff, David P. and Yang, Guang},
  title =	{{Separating k-Player from t-Player One-Way Communication, with Applications to Data Streams}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{97:1--97:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.97},
  URN =		{urn:nbn:de:0030-drops-106733},
  doi =		{10.4230/LIPIcs.ICALP.2019.97},
  annote =	{Keywords: Communication complexity, multi-player communication, one-way communication, streaming complexity}
}
Document
Extended Abstract
DOI: 10.4230/LIPIcs.CCC.2015.582
Incompressible Functions, Relative-Error Extractors, and the Power of Nondeterministic Reductions (Extended Abstract)

Authors: Benny Applebaum, Sergei Artemenko, Ronen Shaltiel, and Guang Yang

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

Abstract
A circuit C compresses a function f:{0,1}^n -> {0,1}^m if given an input x in {0,1}^n the circuit C can shrink x to a shorter l-bit string x' such that later, a computationally-unbounded solver D will be able to compute f(x) based on x'. In this paper we study the existence of functions which are incompressible by circuits of some fixed polynomial size s=n^c. Motivated by cryptographic applications, we focus on average-case (l,epsilon) incompressibility, which guarantees that on a random input x in {0,1}^n, for every size s circuit C:{0,1}^n -> {0,1}^l and any unbounded solver D, the success probability Pr_x[D(C(x))=f(x)] is upper-bounded by 2^(-m)+epsilon. While this notion of incompressibility appeared in several works (e.g., Dubrov and Ishai, STOC 06), so far no explicit constructions of efficiently computable incompressible functions were known. In this work we present the following results: 1. Assuming that E is hard for exponential size nondeterministic circuits, we construct a polynomial time computable boolean function f:{0,1}^n -> {0,1} which is incompressible by size n^c circuits with communication l=(1-o(1)) * n and error epsilon=n^(-c). Our technique generalizes to the case of PRGs against nonboolean circuits, improving and simplifying the previous construction of Shaltiel and Artemenko (STOC 14). 2. We show that it is possible to achieve negligible error parameter epsilon=n^(-omega(1)) for nonboolean functions. Specifically, assuming that E is hard for exponential size Sigma_3-circuits, we construct a nonboolean function f:{0,1}^n -> {0,1}^m which is incompressible by size n^c circuits with l=Omega(n) and extremely small epsilon=n^(-c) * 2^(-m). Our construction combines the techniques of Trevisan and Vadhan (FOCS 00) with a new notion of relative error deterministic extractor which may be of independent interest. 3. We show that the task of constructing an incompressible boolean function f:{0,1}^n -> {0,1} with negligible error parameter epsilon cannot be achieved by "existing proof techniques". Namely, nondeterministic reductions (or even Sigma_i reductions) cannot get epsilon=n^(-omega(1)) for boolean incompressible functions. Our results also apply to constructions of standard Nisan-Wigderson type PRGs and (standard) boolean functions that are hard on average, explaining, in retrospective, the limitations of existing constructions. Our impossibility result builds on an approach of Shaltiel and Viola (SIAM J. Comp., 2010).
Cite as

Benny Applebaum, Sergei Artemenko, Ronen Shaltiel, and Guang Yang. Incompressible Functions, Relative-Error Extractors, and the Power of Nondeterministic Reductions (Extended Abstract). In 30th Conference on Computational Complexity (CCC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 33, pp. 582-600, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

Copy BibTex To Clipboard

@InProceedings{applebaum_et_al:LIPIcs.CCC.2015.582,
  author =	{Applebaum, Benny and Artemenko, Sergei and Shaltiel, Ronen and Yang, Guang},
  title =	{{Incompressible Functions, Relative-Error Extractors, and the Power of Nondeterministic Reductions}},
  booktitle =	{30th Conference on Computational Complexity (CCC 2015)},
  pages =	{582--600},
  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.2015.582},
  URN =		{urn:nbn:de:0030-drops-50567},
  doi =		{10.4230/LIPIcs.CCC.2015.582},
  annote =	{Keywords: compression, pseudorandomness, extractors, nondeterministic reductions}
}
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact