34 Search Results for "Li, Shu-Chen"

Document
Invited Talk
DOI: 10.4230/LIPIcs.ICDT.2024.2
How Database Theory Helps Teach Relational Queries in Database Education (Invited Talk)

Authors: Sudeepa Roy, Amir Gilad, Yihao Hu, Hanze Meng, Zhengjie Miao, Kristin Stephens-Martinez, and Jun Yang

Published in: LIPIcs, Volume 290, 27th International Conference on Database Theory (ICDT 2024)

Abstract
Data analytics skills have become an indispensable part of any education that seeks to prepare its students for the modern workforce. Essential in this skill set is the ability to work with structured relational data. Relational queries are based on logic and may be declarative in nature, posing new challenges to novices and students. Manual teaching resources being limited and enrollment growing rapidly, automated tools that help students debug queries and explain errors are potential game-changers in database education. We present a suite of tools built on the foundations of database theory that has been used by over 1600 students in database classes at Duke University, showcasing a high-impact application of database theory in database education.
Cite as

Sudeepa Roy, Amir Gilad, Yihao Hu, Hanze Meng, Zhengjie Miao, Kristin Stephens-Martinez, and Jun Yang. How Database Theory Helps Teach Relational Queries in Database Education (Invited Talk). In 27th International Conference on Database Theory (ICDT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 290, pp. 2:1-2:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{roy_et_al:LIPIcs.ICDT.2024.2,
  author =	{Roy, Sudeepa and Gilad, Amir and Hu, Yihao and Meng, Hanze and Miao, Zhengjie and Stephens-Martinez, Kristin and Yang, Jun},
  title =	{{How Database Theory Helps Teach Relational Queries in Database Education}},
  booktitle =	{27th International Conference on Database Theory (ICDT 2024)},
  pages =	{2:1--2:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-312-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{290},
  editor =	{Cormode, Graham and Shekelyan, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2024.2},
  URN =		{urn:nbn:de:0030-drops-197841},
  doi =		{10.4230/LIPIcs.ICDT.2024.2},
  annote =	{Keywords: Query Debugging, SQL, Relational Algebra, Relational Calculus, Database Education, Boolean Provenance}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.33
Testing Intersecting and Union-Closed Families

Authors: Xi Chen, Anindya De, Yuhao Li, Shivam Nadimpalli, and Rocco A. Servedio

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
Inspired by the classic problem of Boolean function monotonicity testing, we investigate the testability of other well-studied properties of combinatorial finite set systems, specifically intersecting families and union-closed families. A function f: {0,1}ⁿ → {0,1} is intersecting (respectively, union-closed) if its set of satisfying assignments corresponds to an intersecting family (respectively, a union-closed family) of subsets of [n]. Our main results are that - in sharp contrast with the property of being a monotone set system - the property of being an intersecting set system, and the property of being a union-closed set system, both turn out to be information-theoretically difficult to test. We show that: - For ε ≥ Ω(1/√n), any non-adaptive two-sided ε-tester for intersectingness must make 2^{Ω(n^{1/4}/√{ε})} queries. We also give a 2^{Ω(√{n log(1/ε)})}-query lower bound for non-adaptive one-sided ε-testers for intersectingness. - For ε ≥ 1/2^{Ω(n^{0.49})}, any non-adaptive two-sided ε-tester for union-closedness must make n^{Ω(log(1/ε))} queries. Thus, neither intersectingness nor union-closedness shares the poly(n,1/ε)-query non-adaptive testability that is enjoyed by monotonicity. To complement our lower bounds, we also give a simple poly(n^{√{nlog(1/ε)}},1/ε)-query, one-sided, non-adaptive algorithm for ε-testing each of these properties (intersectingness and union-closedness). We thus achieve nearly tight upper and lower bounds for two-sided testing of intersectingness when ε = Θ(1/√n), and for one-sided testing of intersectingness when ε = Θ(1).
Cite as

Xi Chen, Anindya De, Yuhao Li, Shivam Nadimpalli, and Rocco A. Servedio. Testing Intersecting and Union-Closed Families. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 33:1-33:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chen_et_al:LIPIcs.ITCS.2024.33,
  author =	{Chen, Xi and De, Anindya and Li, Yuhao and Nadimpalli, Shivam and Servedio, Rocco A.},
  title =	{{Testing Intersecting and Union-Closed Families}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{33:1--33:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.33},
  URN =		{urn:nbn:de:0030-drops-195610},
  doi =		{10.4230/LIPIcs.ITCS.2024.33},
  annote =	{Keywords: Sublinear algorithms, property testing, computational complexity, monotonicity, intersecting families, union-closed families}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.75
Total NP Search Problems with Abundant Solutions

Authors: Jiawei Li

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
We define a new complexity class TFAP to capture TFNP problems that possess abundant solutions for each input. We identify several problems across diverse fields that belong to TFAP, including WeakPigeon (finding a collision in a mapping from [2n] pigeons to [n] holes), Yamakawa-Zhandry’s problem [Takashi Yamakawa and Mark Zhandry, 2022], and all problems in TFZPP. Conversely, we introduce the notion of "semi-gluability" to characterize TFNP problems that could have a unique or a very limited number of solutions for certain inputs. We prove that there is no black-box reduction from any "semi-gluable" problems to any TFAP problems. Furthermore, it can be extended to rule out randomized black-box reduction in most cases. We identify that the majority of common TFNP subclasses, including PPA, PPAD, PPADS, PPP, PLS, CLS, SOPL, and UEOPL, are "semi-gluable". This leads to a broad array of oracle separation results within TFNP regime. As a corollary, UEOPL^O ⊈ PWPP^O relative to an oracle O.
Cite as

Jiawei Li. Total NP Search Problems with Abundant Solutions. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 75:1-75:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{li:LIPIcs.ITCS.2024.75,
  author =	{Li, Jiawei},
  title =	{{Total NP Search Problems with Abundant Solutions}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{75:1--75:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.75},
  URN =		{urn:nbn:de:0030-drops-196031},
  doi =		{10.4230/LIPIcs.ITCS.2024.75},
  annote =	{Keywords: TFNP, Pigeonhole Principle}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.29
Effective Resistances in Non-Expander Graphs

Authors: Dongrun Cai, Xue Chen, and Pan Peng

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
Effective resistances are ubiquitous in graph algorithms and network analysis. For an undirected graph G, its effective resistance R_G(s,t) between two vertices s and t is defined as the equivalent resistance between s and t if G is thought of as an electrical network with unit resistance on each edge. If we use L_G to denote the Laplacian matrix of G and L_G^† to denote its pseudo-inverse, we have R_G(s,t) = (𝟏_s-𝟏_t)^⊤ L^† (𝟏_s-𝟏_t) such that classical Laplacian solvers [Daniel A. Spielman and Shang{-}Hua Teng, 2014] provide almost-linear time algorithms to approximate R_G(s,t). In this work, we study sublinear time algorithms to approximate the effective resistance of an adjacent pair s and t. We consider the classical adjacency list model [Ron, 2019] for local algorithms. While recent works [Andoni et al., 2018; Peng et al., 2021; Li and Sachdeva, 2023] have provided sublinear time algorithms for expander graphs, we prove several lower bounds for general graphs of n vertices and m edges: 1) It needs Ω(n) queries to obtain 1.01-approximations of the effective resistance of an adjacent pair s and t, even for graphs of degree at most 3 except s and t. 2) For graphs of degree at most d and any parameter 𝓁, it needs Ω(m/𝓁) queries to obtain c ⋅ min{d,𝓁}-approximations where c > 0 is a universal constant. Moreover, we supplement the first lower bound by providing a sublinear time (1+ε)-approximation algorithm for graphs of degree 2 except the pair s and t. One of our technical ingredients is to bound the expansion of a graph in terms of the smallest non-trivial eigenvalue of its Laplacian matrix after removing edges. We discover a new lower bound on the eigenvalues of perturbed graphs (resp. perturbed matrices) by incorporating the effective resistance of the removed edge (resp. the leverage scores of the removed rows), which may be of independent interest.
Cite as

Dongrun Cai, Xue Chen, and Pan Peng. Effective Resistances in Non-Expander Graphs. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cai_et_al:LIPIcs.ESA.2023.29,
  author =	{Cai, Dongrun and Chen, Xue and Peng, Pan},
  title =	{{Effective Resistances in Non-Expander Graphs}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.29},
  URN =		{urn:nbn:de:0030-drops-186823},
  doi =		{10.4230/LIPIcs.ESA.2023.29},
  annote =	{Keywords: Sublinear Time Algorithm, Effective Resistance, Leverage Scores, Matrix Perturbation}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.97
Improved Algorithms for Online Rent Minimization Problem Under Unit-Size Jobs

Authors: Enze Sun, Zonghan Yang, and Yuhao Zhang

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
We consider the Online Rent Minimization problem, where online jobs with release times, deadlines, and processing times must be scheduled on machines that can be rented for a fixed length period of T. The objective is to minimize the number of machine rents. This problem generalizes the Online Machine Minimization problem where machines can be rented for an infinite period, and both problems have an asymptotically optimal competitive ratio of O(log(p_max/p_min)) for general processing times, where p_max and p_min are the maximum and minimum processing times respectively. However, for small values of p_max/p_min, a better competitive ratio can be achieved by assuming unit-size jobs. Under this assumption, Devanur et al. (2014) gave an optimal e-competitive algorithm for Online Machine Minimization, and Chen and Zhang (2022) gave a (3e+7) ≈ 15.16-competitive algorithm for Online Rent Minimization. In this paper, we significantly improve the competitive ratio of the Online Rent Minimization problem under unit size to 6, by using a clean oracle-based online algorithm framework.
Cite as

Enze Sun, Zonghan Yang, and Yuhao Zhang. Improved Algorithms for Online Rent Minimization Problem Under Unit-Size Jobs. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 97:1-97:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{sun_et_al:LIPIcs.ESA.2023.97,
  author =	{Sun, Enze and Yang, Zonghan and Zhang, Yuhao},
  title =	{{Improved Algorithms for Online Rent Minimization Problem Under Unit-Size Jobs}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{97:1--97:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.97},
  URN =		{urn:nbn:de:0030-drops-187500},
  doi =		{10.4230/LIPIcs.ESA.2023.97},
  annote =	{Keywords: Online Algorithm, Scheduling, Machine Minimization, Rent Minimization}
}
Document
DOI: 10.4230/LIPIcs.CCC.2023.21
Reducing Tarski to Unique Tarski (In the Black-Box Model)

Authors: Xi Chen, Yuhao Li, and Mihalis Yannakakis

Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)

Abstract
We study the problem of finding a Tarski fixed point over the k-dimensional grid [n]^k. We give a black-box reduction from the Tarski problem to the same problem with an additional promise that the input function has a unique fixed point. It implies that the Tarski problem and the unique Tarski problem have exactly the same query complexity. Our reduction is based on a novel notion of partial-information functions which we use to fool algorithms for the unique Tarski problem as if they were working on a monotone function with a unique fixed point.
Cite as

Xi Chen, Yuhao Li, and Mihalis Yannakakis. Reducing Tarski to Unique Tarski (In the Black-Box Model). In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 21:1-21:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chen_et_al:LIPIcs.CCC.2023.21,
  author =	{Chen, Xi and Li, Yuhao and Yannakakis, Mihalis},
  title =	{{Reducing Tarski to Unique Tarski (In the Black-Box Model)}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{21:1--21:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.21},
  URN =		{urn:nbn:de:0030-drops-182919},
  doi =		{10.4230/LIPIcs.CCC.2023.21},
  annote =	{Keywords: Tarski fixed point, Query complexity, TFNP}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICALP.2023.2
An Almost-Linear Time Algorithm for Maximum Flow and More (Invited Talk)

Authors: Rasmus Kyng

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

Abstract
In this talk, I will explain a new algorithm for computing exact maximum and minimum-cost flows in almost-linear time, settling the time complexity of these basic graph problems up to subpolynomial factors. Our algorithm uses a novel interior point method that builds the optimal flow as a sequence of approximate minimum-ratio cycles, each of which is computed and processed very efficiently using a new dynamic data structure. By well-known reductions, our result implies almost-linear time algorithms for several problems including bipartite matching, optimal transport, and undirected vertex connectivity. Our framework also extends to minimizing general edge-separable convex functions to high accuracy, yielding the first almost-linear time algorithms for many other problems including entropy-regularized optimal transport, matrix scaling, p-norm flows, and isotonic regression. This talk is based on joint work with Li Chen, Yang P. Liu, Richard Peng, Maximilian Probst Gutenberg, and Sushant Sachdeva [Chen et al., 2022]. Our result appeared in FOCS'22 and won the FOCS best paper award.
Cite as

Rasmus Kyng. An Almost-Linear Time Algorithm for Maximum Flow and More (Invited Talk). In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{kyng:LIPIcs.ICALP.2023.2,
  author =	{Kyng, Rasmus},
  title =	{{An Almost-Linear Time Algorithm for Maximum Flow and More}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{2:1--2:1},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.2},
  URN =		{urn:nbn:de:0030-drops-180543},
  doi =		{10.4230/LIPIcs.ICALP.2023.2},
  annote =	{Keywords: Maximum flow, Minimum cost flow, Data structures, Interior point methods, Convex optimization}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.35
Black-Box Constructive Proofs Are Unavoidable

Authors: Lijie Chen, Ryan Williams, and Tianqi Yang

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
Following Razborov and Rudich, a "natural property" for proving a circuit lower bound satisfies three axioms: constructivity, largeness, and usefulness. In 2013, Williams proved that for any reasonable circuit class C, NEXP ⊂ C is equivalent to the existence of a constructive property useful against C. Here, a property is constructive if it can be decided in poly(N) time, where N = 2ⁿ is the length of the truth-table of the given n-input function. Recently, Fan, Li, and Yang initiated the study of black-box natural properties, which require a much stronger notion of constructivity, called black-box constructivity: the property should be decidable in randomized polylog(N) time, given oracle access to the n-input function. They showed that most proofs based on random restrictions yield black-box natural properties, and demonstrated limitations on what black-box natural properties can prove. In this paper, perhaps surprisingly, we prove that the equivalence of Williams holds even with this stronger notion of black-box constructivity: for any reasonable circuit class C, NEXP ⊂ C is equivalent to the existence of a black-box constructive property useful against C. The main technical ingredient in proving this equivalence is a smooth, strong, and locally-decodable probabilistically checkable proof (PCP), which we construct based on a recent work by Paradise. As a by-product, we show that average-case witness lower bounds for PCP verifiers follow from NEXP lower bounds. We also show that randomness is essential in the definition of black-box constructivity: we unconditionally prove that there is no deterministic polylog(N)-time constructive property that is useful against even polynomial-size AC⁰ circuits.
Cite as

Lijie Chen, Ryan Williams, and Tianqi Yang. Black-Box Constructive Proofs Are Unavoidable. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 35:1-35:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chen_et_al:LIPIcs.ITCS.2023.35,
  author =	{Chen, Lijie and Williams, Ryan and Yang, Tianqi},
  title =	{{Black-Box Constructive Proofs Are Unavoidable}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{35:1--35:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.35},
  URN =		{urn:nbn:de:0030-drops-175380},
  doi =		{10.4230/LIPIcs.ITCS.2023.35},
  annote =	{Keywords: Circuit lower bounds, natural proofs, probabilistic checkable proofs}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.52
Budget Pacing in Repeated Auctions: Regret and Efficiency Without Convergence

Authors: Jason Gaitonde, Yingkai Li, Bar Light, Brendan Lucier, and Aleksandrs Slivkins

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
Online advertising via auctions increasingly dominates the marketing landscape. A typical advertiser may participate in thousands of auctions each day with bids tailored to a variety of signals about user demographics and intent. These auctions are strategically linked through a global budget constraint. To help address the difficulty of bidding, many major online platforms now provide automated budget management via a flexible approach called budget pacing: rather than bidding directly, an advertiser specifies a global budget target and a maximum willingness-to-pay for different types of advertising opportunities. The specified maximums are then scaled down (or "paced") by a multiplier so that the realized total spend matches the target budget. These automated bidders are now near-universally adopted across all mature advertising platforms, raising pressing questions about market outcomes that arise when advertisers use budget pacing simultaneously. In this paper we study the aggregate welfare and individual regret guarantees of dynamic pacing algorithms in repeated auctions with budgets. We show that when agents simultaneously use a natural form of gradient-based pacing, the liquid welfare obtained over the course of the dynamics is at least half the optimal liquid welfare obtainable by any allocation rule, matching the best possible bound for static auctions even in pure Nash equilibria [Aggarwal et al., WINE 2019; Babaioff et al., ITCS 2021]. In contrast to prior work, these results hold without requiring convergence of the dynamics, circumventing known computational obstacles of finding equilibria [Chen et al., EC 2021]. Our result is robust to the correlation structure among agents' valuations and holds for any core auction, a broad class that includes first-price, second-price, and GSP auctions. We complement the aggregate guarantees by showing that an agent using such pacing algorithms achieves an O(T^{3/4}) regret relative to the value obtained by the best fixed pacing multiplier in hindsight in stochastic bidding environments. Compared to past work, this result applies to more general auctions and extends to adversarial settings with respect to dynamic regret.
Cite as

Jason Gaitonde, Yingkai Li, Bar Light, Brendan Lucier, and Aleksandrs Slivkins. Budget Pacing in Repeated Auctions: Regret and Efficiency Without Convergence. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, p. 52:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gaitonde_et_al:LIPIcs.ITCS.2023.52,
  author =	{Gaitonde, Jason and Li, Yingkai and Light, Bar and Lucier, Brendan and Slivkins, Aleksandrs},
  title =	{{Budget Pacing in Repeated Auctions: Regret and Efficiency Without Convergence}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{52:1--52:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.52},
  URN =		{urn:nbn:de:0030-drops-175557},
  doi =		{10.4230/LIPIcs.ITCS.2023.52},
  annote =	{Keywords: repeated auctions with budgets, pacing, learning in auctions}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2022.4
Greedy Algorithms for the Freight Consolidation Problem

Authors: Zuguang Gao, John R. Birge, Richard Li-Yang Chen, and Maurice Cheung

Published in: OASIcs, Volume 106, 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)

Abstract
We define and study the (ocean) freight consolidation problem (FCP), which plays a crucial role in solving today’s supply chain crisis. Roughly speaking, every day and every hour, a freight forwarder sees a set of shipments and a set of containers at the origin port. There is a shipment cost associated with assigning each shipment to each container. If a container is assigned any shipment, there is also a procurement cost for that container. The FCP aims to minimize the total cost of fulfilling all the shipments, subject to capacity constraints of the containers. In this paper, we show that no constant factor approximation exists for FCP, and propose a series of greedy based heuristics for solving the problem. We also test our heuristics with simulated data and show that our heuristics achieve small optimality gaps.
Cite as

Zuguang Gao, John R. Birge, Richard Li-Yang Chen, and Maurice Cheung. Greedy Algorithms for the Freight Consolidation Problem. In 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022). Open Access Series in Informatics (OASIcs), Volume 106, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gao_et_al:OASIcs.ATMOS.2022.4,
  author =	{Gao, Zuguang and Birge, John R. and Chen, Richard Li-Yang and Cheung, Maurice},
  title =	{{Greedy Algorithms for the Freight Consolidation Problem}},
  booktitle =	{22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)},
  pages =	{4:1--4:19},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-259-4},
  ISSN =	{2190-6807},
  year =	{2022},
  volume =	{106},
  editor =	{D'Emidio, Mattia and Lindner, Niels},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2022.4},
  URN =		{urn:nbn:de:0030-drops-171086},
  doi =		{10.4230/OASIcs.ATMOS.2022.4},
  annote =	{Keywords: Freight consolidation, heuristics, greedy algorithm}
}
Document
DOI: 10.4230/LIPIcs.CCC.2022.19
The Composition Complexity of Majority

Authors: Victor Lecomte, Prasanna Ramakrishnan, and Li-Yang Tan

Published in: LIPIcs, Volume 234, 37th Computational Complexity Conference (CCC 2022)

Abstract
We study the complexity of computing majority as a composition of local functions: Maj_n = h(g_1,…,g_m), where each g_j: {0,1}ⁿ → {0,1} is an arbitrary function that queries only k ≪ n variables and h: {0,1}^m → {0,1} is an arbitrary combining function. We prove an optimal lower bound of m ≥ Ω(n/k log k) on the number of functions needed, which is a factor Ω(log k) larger than the ideal m = n/k. We call this factor the composition overhead; previously, no superconstant lower bounds on it were known for majority. Our lower bound recovers, as a corollary and via an entirely different proof, the best known lower bound for bounded-width branching programs for majority (Alon and Maass '86, Babai et al. '90). It is also the first step in a plan that we propose for breaking a longstanding barrier in lower bounds for small-depth boolean circuits. Novel aspects of our proof include sharp bounds on the information lost as computation flows through the inner functions g_j, and the bootstrapping of lower bounds for a multi-output function (Hamming weight) into lower bounds for a single-output one (majority).
Cite as

Victor Lecomte, Prasanna Ramakrishnan, and Li-Yang Tan. The Composition Complexity of Majority. In 37th Computational Complexity Conference (CCC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 234, pp. 19:1-19:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lecomte_et_al:LIPIcs.CCC.2022.19,
  author =	{Lecomte, Victor and Ramakrishnan, Prasanna and Tan, Li-Yang},
  title =	{{The Composition Complexity of Majority}},
  booktitle =	{37th Computational Complexity Conference (CCC 2022)},
  pages =	{19:1--19:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-241-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{234},
  editor =	{Lovett, Shachar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2022.19},
  URN =		{urn:nbn:de:0030-drops-165818},
  doi =		{10.4230/LIPIcs.CCC.2022.19},
  annote =	{Keywords: computational complexity, circuit lower bounds}
}
Document
DOI: 10.4230/LIPIcs.CCC.2022.23
Extremely Efficient Constructions of Hash Functions, with Applications to Hardness Magnification and PRFs

Authors: Lijie Chen, Jiatu Li, and Tianqi Yang

Published in: LIPIcs, Volume 234, 37th Computational Complexity Conference (CCC 2022)

Abstract
In a recent work, Fan, Li, and Yang (STOC 2022) constructed a family of almost-universal hash functions such that each function in the family is computable by (2n + o(n))-gate circuits of fan-in 2 over the B₂ basis. Applying this family, they established the existence of pseudorandom functions computable by circuits of the same complexity, under the standard assumption that OWFs exist. However, a major disadvantage of the hash family construction by Fan, Li, and Yang (STOC 2022) is that it requires a seed length of poly(n), which limits its potential applications. We address this issue by giving an improved construction of almost-universal hash functions with seed length polylog(n), such that each function in the family is computable with POLYLOGTIME-uniform (2n + o(n))-gate circuits. Our new construction has the following applications in both complexity theory and cryptography. - (Hardness magnification). Let α : ℕ → ℕ be any function such that α(n) ≤ log n / log log n. We show that if there is an n^{α(n)}-sparse NP language that does not have probabilistic circuits of 2n + O(n/log log n) gates, then we have (1) NTIME[2ⁿ] ⊈ SIZE[2^{n^{1/5}}] and (2) NP ⊈ SIZE[n^k] for every constant k. Complementing this magnification phenomenon, we present an O(n)-sparse language in P which requires probabilistic circuits of size at least 2n - 2. This is the first result in hardness magnification showing that even a sub-linear additive improvement on known circuit size lower bounds would imply NEXP ⊄ P_{/poly}. Following Chen, Jin, and Williams (STOC 2020), we also establish a sharp threshold for explicit obstructions: we give an explict obstruction against (2n-2)-size circuits, and prove that a sub-linear additive improvement on the circuit size would imply (1) DTIME[2ⁿ] ⊈ SIZE[2^{n^{1/5}}] and (2) P ⊈ SIZE[n^k] for every constant k. - (Extremely efficient construction of pseudorandom functions). Assuming that one of integer factoring, decisional Diffie-Hellman, or ring learning-with-errors is sub-exponentially hard, we show the existence of pseudorandom functions computable by POLYLOGTIME-uniform AC⁰[2] circuits with 2n + o(n) wires, with key length polylog(n). We also show that PRFs computable by POLYLOGTIME-uniform B₂ circuits of 2n + o(n) gates follows from the existence of sub-exponentially secure one-way functions.
Cite as

Lijie Chen, Jiatu Li, and Tianqi Yang. Extremely Efficient Constructions of Hash Functions, with Applications to Hardness Magnification and PRFs. In 37th Computational Complexity Conference (CCC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 234, pp. 23:1-23:37, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chen_et_al:LIPIcs.CCC.2022.23,
  author =	{Chen, Lijie and Li, Jiatu and Yang, Tianqi},
  title =	{{Extremely Efficient Constructions of Hash Functions, with Applications to Hardness Magnification and PRFs}},
  booktitle =	{37th Computational Complexity Conference (CCC 2022)},
  pages =	{23:1--23:37},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-241-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{234},
  editor =	{Lovett, Shachar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2022.23},
  URN =		{urn:nbn:de:0030-drops-165852},
  doi =		{10.4230/LIPIcs.CCC.2022.23},
  annote =	{Keywords: Almost universal hash functions, hardness magnification, pseudorandom functions}
}
Document
DOI: 10.4230/LIPIcs.CCC.2022.34
Improved Pseudorandom Generators for AC⁰ Circuits

Authors: Xin Lyu

Published in: LIPIcs, Volume 234, 37th Computational Complexity Conference (CCC 2022)

Abstract
We give PRG for depth-d, size-m AC⁰ circuits with seed length O(log^{d-1}(m)log(m/ε)log log(m)). Our PRG improves on previous work [Luca Trevisan and Tongke Xue, 2013; Rocco A. Servedio and Li-Yang Tan, 2019; Zander Kelley, 2021] from various aspects. It has optimal dependence on 1/ε and is only one "log log(m)" away from the lower bound barrier. For the case of d = 2, the seed length tightly matches the best-known PRG for CNFs [Anindya De et al., 2010; Avishay Tal, 2017]. There are two technical ingredients behind our new result; both of them might be of independent interest. First, we use a partitioning-based approach to construct PRGs based on restriction lemmas for AC⁰. Previous works [Luca Trevisan and Tongke Xue, 2013; Rocco A. Servedio and Li-Yang Tan, 2019; Zander Kelley, 2021] usually built PRGs on the Ajtai-Wigderson framework [Miklós Ajtai and Avi Wigderson, 1989]. Compared with them, the partitioning approach avoids the extra "log(n)" factor that usually arises from the Ajtai-Wigderson framework, allowing us to get the almost-tight seed length. The partitioning approach is quite general, and we believe it can help design PRGs for classes beyond constant-depth circuits. Second, improving and extending [Luca Trevisan and Tongke Xue, 2013; Rocco A. Servedio and Li-Yang Tan, 2019; Zander Kelley, 2021], we prove a full derandomization of the powerful multi-switching lemma [Johan Håstad, 2014]. We show that one can use a short random seed to sample a restriction, such that a family of DNFs simultaneously simplifies under the restriction with high probability. This answers an open question in [Zander Kelley, 2021]. Previous derandomizations were either partial (that is, they pseudorandomly choose variables to restrict, and then fix those variables to truly-random bits) or had sub-optimal seed length. In our application, having a fully-derandomized switching lemma is crucial, and the randomness-efficiency of our derandomization allows us to get an almost-tight seed length.
Cite as

Xin Lyu. Improved Pseudorandom Generators for AC⁰ Circuits. In 37th Computational Complexity Conference (CCC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 234, pp. 34:1-34:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lyu:LIPIcs.CCC.2022.34,
  author =	{Lyu, Xin},
  title =	{{Improved Pseudorandom Generators for AC⁰ Circuits}},
  booktitle =	{37th Computational Complexity Conference (CCC 2022)},
  pages =	{34:1--34:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-241-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{234},
  editor =	{Lovett, Shachar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2022.34},
  URN =		{urn:nbn:de:0030-drops-165963},
  doi =		{10.4230/LIPIcs.CCC.2022.34},
  annote =	{Keywords: pseudorandom generators, derandomization, switching Lemmas, AC⁰}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.43
Improved Decoding of Expander Codes

Authors: Xue Chen, Kuan Cheng, Xin Li, and Minghui Ouyang

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
We study the classical expander codes, introduced by Sipser and Spielman [M. Sipser and D. A. Spielman, 1996]. Given any constants 0 < α, ε < 1/2, and an arbitrary bipartite graph with N vertices on the left, M < N vertices on the right, and left degree D such that any left subset S of size at most α N has at least (1-ε)|S|D neighbors, we show that the corresponding linear code given by parity checks on the right has distance at least roughly {α N}/{2 ε}. This is strictly better than the best known previous result of 2(1-ε) α N [Madhu Sudan, 2000; Viderman, 2013] whenever ε < 1/2, and improves the previous result significantly when ε is small. Furthermore, we show that this distance is tight in general, thus providing a complete characterization of the distance of general expander codes. Next, we provide several efficient decoding algorithms, which vastly improve previous results in terms of the fraction of errors corrected, whenever ε < 1/4. Finally, we also give a bound on the list-decoding radius of general expander codes, which beats the classical Johnson bound in certain situations (e.g., when the graph is almost regular and the code has a high rate). Our techniques exploit novel combinatorial properties of bipartite expander graphs. In particular, we establish a new size-expansion tradeoff, which may be of independent interests.
Cite as

Xue Chen, Kuan Cheng, Xin Li, and Minghui Ouyang. Improved Decoding of Expander Codes. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 43:1-43:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chen_et_al:LIPIcs.ITCS.2022.43,
  author =	{Chen, Xue and Cheng, Kuan and Li, Xin and Ouyang, Minghui},
  title =	{{Improved Decoding of Expander Codes}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{43:1--43:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.43},
  URN =		{urn:nbn:de:0030-drops-156394},
  doi =		{10.4230/LIPIcs.ITCS.2022.43},
  annote =	{Keywords: Expander Code, Decoding}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.48
Streaming Algorithms for Graph k-Matching with Optimal or Near-Optimal Update Time

Authors: Jianer Chen, Qin Huang, Iyad Kanj, Qian Li, and Ge Xia

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
We present streaming algorithms for the graph k-matching problem in both the insert-only and dynamic models. Our algorithms, while keeping the space complexity matching the best known upper bound, have optimal or near-optimal update time, significantly improving on previous results. More specifically, for the insert-only streaming model, we present a one-pass randomized algorithm that runs in optimal 𝒪(k²) space and has optimal 𝒪(1) update time, and that, w.h.p. (with high probability), computes a maximum weighted k-matching of a weighted graph. Previously, the best upper bound on the update time was 𝒪(log k), which was achieved by a deterministic streaming algorithm that however only works for unweighted graphs [Stefan Fafianie and Stefan Kratsch, 2014]. For the dynamic streaming model, we present a one-pass randomized algorithm that, w.h.p., computes a maximum weighted k-matching of a weighted graph in Õ(Wk²) space and with Õ(1) update time, where W is the number of distinct edge weights. Again the update time of our algorithm improves the previous best upper bound Õ(k²) [Rajesh Chitnis et al., 2016]. Moreover, we prove that in the dynamic streaming model, any randomized streaming algorithm for the problem requires k²⋅ Ω(W(log W+1)) bits of space. Hence, both the space and update-time complexities achieved by our algorithm in the dynamic model are near-optimal. A streaming approximation algorithm for k-matching is also presented, whose space complexity matches the best known upper bound with a significantly improved update time.
Cite as

Jianer Chen, Qin Huang, Iyad Kanj, Qian Li, and Ge Xia. Streaming Algorithms for Graph k-Matching with Optimal or Near-Optimal Update Time. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 48:1-48:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{chen_et_al:LIPIcs.ISAAC.2021.48,
  author =	{Chen, Jianer and Huang, Qin and Kanj, Iyad and Li, Qian and Xia, Ge},
  title =	{{Streaming Algorithms for Graph k-Matching with Optimal or Near-Optimal Update Time}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{48:1--48:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.48},
  URN =		{urn:nbn:de:0030-drops-154816},
  doi =		{10.4230/LIPIcs.ISAAC.2021.48},
  annote =	{Keywords: streaming algorithms, matching, parameterized algorithms, lower bounds}
}
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