Searcharxiv⌕ Search

arXiv subjects

Yaonan Jin

Publications and source records attributed to Yaonan Jin.

At least 19 recordsLinked to original sources
arXiv2026

Benchmark-Tight Approximation Ratio of Simple Mechanism for a Unit-Demand Buyer

We study revenue maximization in the unit-demand single-buyer setting. Our main result is that \textsf{Uniform-Ironed-Virtual-Value Item Pricing} guarantees a {\em tight} $3$-approximation to the \textsf{Duality Relaxation Benchmark} [Chawla-Malec-Sivan, EC'10/GEB'15; Cai-Devanur-Weinberg, STOC'16/ SICOMP'21], breaking the barrier of $4$ since [Chawla-Hartline-Malec-Sivan, STOC'10; Chawla-Malec-Sivan, EC'10/GEB'15]. To our knowledge, this is the first {\em benchmark-tight} revenue guarantee of any simple multi-item mechanism. Technically, all previous works employ \textsf{Myerson Auction} as an intermediary. The barrier of $4$ follows as \textsf{Uniform-Ironed-Virtual-Value Item Pricing} achieves a {\em tight} $2$-approximation to \textsf{Myerson Auction}, which then achieves a {\em tight} $2$-approximation to \textsf{Duality Relaxation Benchmark}. Instead, our new approach avoids \textsf{Myerson Auction}, thus enabling the improvement. Central to our work are a {\em benchmark-based} $3$-competitive prophet inequality and its {\em fully constructive} proof. Such variant prophet inequalities shall find future applications, e.g., to Multi-Item Mechanism Design where optimal revenues are relaxed to various more accessible benchmarks. We complement our benchmark-tight ratio with an impossibility result. All previous works and ours follow the {\em single-dimensional representative} approach introduced by [Chawla-Hartline-Kleinberg, EC'07]. Against \textsf{Duality Relaxation Benchmark}, it turns out that this approach cannot beat our bound of $3$ for a large class of \textsf{Item Pricing}'s.

cs.GT↗
arXiv2026

Tight Regret Bounds for Fixed-Price Bilateral Trade

We examine fixed-price mechanisms in bilateral trade through the lens of regret minimization. Our main results are twofold. (i) For independent values, a near-optimal $\widetildeΘ(T^{2/3})$ tight bound for $\textsf{Global Budget Balance}$ fixed-price mechanisms with two-bit/one-bit feedback. (ii) For correlated/adversarial values, a near-optimal $Ω(T^{3/4})$ lower bound for $\textsf{Global Budget Balance}$ fixed-price mechanisms with two-bit/one-bit feedback, which improves the best known $Ω(T^{5/7})$ lower bound obtained in the work [BCCF24] and, up to polylogarithmic factors, matches the $\widetilde{\mathcal{O}}(T^{3 / 4})$ upper bound obtained in the same work. Our work in combination with the previous works [CCCFL24mor, CCCFL24jmlr, AFF24, BCCF24] (essentially) gives a thorough understanding of regret minimization for fixed-price bilateral trade. En route, we have developed two technical ingredients that might be of independent interest: (i) A novel algorithmic paradigm, called $\textit{fractal elimination}$, to address one-bit feedback and independent values. (ii) A new $\textit{lower-bound construction}$ with novel proof techniques, to address the $\textsf{Global Budget Balance}$ constraint and correlated values.

cs.GT↗
arXiv2026

Fully Dynamic Euclidean k-Means

We consider the Euclidean $k$-means clustering problem in a dynamic setting, where we have to explicitly maintain a solution (a set of $k$ centers) $S \subseteq \mathbb{R}^d$ subject to point insertions/deletions in $\mathbb{R}^d$. We present a dynamic algorithm for Euclidean $k$-means with $\mathrm{poly}(1/ε)$-approximation ratio, $\tilde{O}(k^ε)$ update time, and $\tilde{O}(1)$ recourse, for any $ε\in (0,1)$, even when $d$ and $k$ are both part of the input. This is the first algorithm to achieve a constant ratio with $o(k)$ update time for this problem, whereas the previous $O(1)$-approximation runs in $\tilde O(k)$ update time [Bhattacharya, Costa, Farokhnejad; STOC'25]. In fact, previous algorithms cannot go beyond $O(k)$ update time precisely because they are designed for general metrics where an $Ω(k)$ lower bound is known. We break this $O(k)$ barrier by devising new fundamental data structures to utilize Euclidean properties: a structure that (implicitly) maintains a clustering subject to both center and data point updates, and a range query structure that can evaluate a mergeable function over any metric ball range given as a query. To obtain these structures, we devise the first consistent hashing scheme [Czumaj, Jiang, Krauthgamer, Vesel{ý}, Yang; FOCS'22] that achieves $\tilde O(n^ε)$ running time per point evaluation with competitive parameters. Our final algorithm exploits the framework of [Bhattacharya, Costa, Farokhnejad; STOC'25] for general metrics. The key change is to redesign several critical subroutines so that they reduce to our new Euclidean data structures, replacing the general-metric implementations that are unlikely to run efficiently even when Euclidean properties are provided.

cs.DS↗
arXiv2026

Round-efficient Fully-scalable MPC algorithms for k-Means

We study Euclidean $k$-Means under the Massively Parallel Computation (MPC) model, focusing on the \emph{fully-scalable} setting. Our main result is a fully-scalable $O((\log n/\log\log n)^2)$-approximation in $O(1)$ rounds. Previously, fully-scalable algorithms for $k$-Means either run in super-constant $O(\log\log n \cdot \log\log\log n)$ rounds, albeit with a better $O(1)$-approximation [Cohen-Addad et al., SODA'26], or suffer from bicriteria guarantees [Bhaskara and Wijewardena, ICML'18; Czumaj et al., ICALP'24]. Our algorithm also gives an $O(\log n/\log\log n)$-approximation for $k$-Median, which improves a recent $O(\log n)$-approximation [Goranci et al., SODA'26], and this $o(\log n)$ ratio breaks the fundamental barrier of tree embedding methods used therein. Our main technical contribution is a new variant of the MP algorithm [Mettu and Plaxton, SICOMP'03] that works for general metrics, whose new guarantee is the Lagrangian Multiplier Preserving (LMP) property, which, importantly, holds even under arbitrary distance distortions. Allowing distance distortion is crucial for efficient MPC implementations and useful for efficient algorithm design in general, whereas preserving the LMP property under distance distortion is known to be a significant technical challenge. As a byproduct of our techniques, we also obtain an $O(1)$-approximation to the optimal \emph{value} in $O(1)$ rounds, which conceptually suggests that achieving a true $O(1)$-approximation (for the solution) in $O(1)$ rounds may be a sensible goal for future study.

cs.DS↗
arXiv2026

The Query Complexity of Uniform Pricing

Real-world pricing mechanisms are typically optimized using training data, a setting corresponding to the \textit{pricing query complexity} problem in Mechanism Design. The previous work [LSTW23] studies the \textit{single-distribution} case, with tight bounds of $\widetildeΘ(\varepsilon^{-3})$ for a \textit{general} distribution and $\widetildeΘ(\varepsilon^{-2})$ for either a \textit{regular} or \textit{monotone-hazard-rate (MHR)} distribution, where $\varepsilon \in (0, 1)$ denotes the (additive) revenue loss of a learned uniform price relative to the Bayesian-optimal uniform price. This can be directly interpreted as ``the query complexity of the {\em \textsf{Uniform Pricing}} mechanism, in the \textit{single-distribution} case''. Yet in the \textit{multi-distribution} case, can the regularity and MHR conditions still lead to improvements over the tight bound $\widetildeΘ(\varepsilon^{-3})$ for general distributions? We answer this question in the negative, by establishing a (near-)matching lower bound $Ω(\varepsilon^{-3})$ for either \textit{two regular distributions} or \textit{three MHR distributions}. We also address the \textit{regret minimization} problem and, in comparison with the folklore upper bound $\widetilde{O}(T^{2 / 3})$ for general distributions (see, e.g., [SW24]), establish a (near-)matching lower bound $Ω(T^{2 / 3})$ for either \textit{two regular distributions} or \textit{three MHR distributions}, via a black-box reduction. Again, this is in stark contrast to the tight bound $\widetildeΘ(T^{1 / 2})$ for a single regular or MHR distribution.

cs.GT↗
arXiv2026

Tight Regret Bounds for Bilateral Trade under Semi Feedback

The study of \textit{regret minimization in fixed-price bilateral trade} has received considerable attention in recent research. Previous works [CCC+24a, CCC+24b, AFF24, BCCF24, CJLZ25, LCM25a, GDFS25] have acquired a thorough understanding of the problem, except for determining the tight regret bound for GBB semi-feedback fixed-price mechanisms under adversarial values. In this paper, we resolve this open question by devising an $\widetilde{O}(T^{2 / 3})$-regret mechanism, matching the $Ω(T^{2 / 3})$ lower bound from [CJLZ25] up to polylogarithmic factors.

cs.GT↗
arXiv2026

Anonymous Pricing in Large Markets

We study revenue maximization when a seller offers $k$ identical units to ex ante heterogeneous, unit-demand buyers. While anonymous pricing can be $Θ(\log k)$ worse than optimal in general multi-unit environments, we show that this pessimism disappears in large markets, where no single buyer accounts for a non-negligible share of optimal revenue. Under (quasi-)regularity, anonymous pricing achieves a $2+O(1/\sqrt{k})$ approximation to the optimal mechanism; the worst-case ratio is maximized at about $2.47$ when $k=1$ and converges to $2$ as $k$ grows. This indicates that the gains from third-degree price discrimination are mild in large markets.

cs.GT↗
arXiv2025

Local Search for Clustering in Almost-linear Time

We propose the first \emph{local search} algorithm for Euclidean clustering that attains an $O(1)$-approximation in almost-linear time. Specifically, for Euclidean $k$-Means, our algorithm achieves an $O(c)$-approximation in $\tilde{O}(n^{1 + 1 / c})$ time, for any constant $c \ge 1$, maintaining the same running time as the previous (non-local-search-based) approach [la Tour and Saulpic, arXiv'2407.11217] while improving the approximation factor from $O(c^{6})$ to $O(c)$. The algorithm generalizes to any metric space with sparse spanners, delivering efficient constant approximation in $\ell_p$ metrics, doubling metrics, Jaccard metrics, etc. This generality derives from our main technical contribution: a local search algorithm on general graphs that obtains an $O(1)$-approximation in almost-linear time. We establish this through a new $1$-swap local search framework featuring a novel swap selection rule. At a high level, this rule ``scores'' every possible swap, based on both its modification to the clustering and its improvement to the clustering objective, and then selects those high-scoring swaps. To implement this, we design a new data structure for maintaining approximate nearest neighbors with amortized guarantees tailored to our framework.

cs.DS↗
arXiv2024

Beyond Regularity: Simple versus Optimal Mechanisms, Revisited

A large proportion of the Bayesian mechanism design literature is restricted to the family of regular distributions $\mathbb{F}_{\tt reg}$ [Mye81] or the family of monotone hazard rate (MHR) distributions $\mathbb{F}_{\tt MHR}$ [BMP63], which overshadows this beautiful and well-developed theory. We (re-)introduce two generalizations, the family of quasi-regular distributions $\mathbb{F}_{\tt Q-reg}$ and the family of quasi-MHR distributions $\mathbb{F}_{\tt Q-MHR}$. All four families together form the following hierarchy: $\mathbb{F}_{\tt MHR} \subsetneq (\mathbb{F}_{\tt reg} \cap \mathbb{F}_{\tt Q-MHR}) \subsetneq \mathbb{F}_{\tt Q-reg}$ and $\mathbb{F}_{\tt Q-MHR} \subsetneq (\mathbb{F}_{\tt reg} \cup \mathbb{F}_{\tt Q-MHR}) \subsetneq \mathbb{F}_{\tt Q-reg}$. The significance of our new families is manifold. First, their defining conditions are immediate relaxations of the regularity/MHR conditions (i.e., monotonicity of the virtual value functions and/or the hazard rate functions), which reflect economic intuition. Second, they satisfy natural mathematical properties (about order statistics) that are violated by both original families $\mathbb{F}_{\tt reg}$ and $\mathbb{F}_{\tt MHR}$. Third but foremost, numerous results [BK96, HR09a, CD15, DRY15, HR14, AHN+19, JLTX20, JLQ+19b, FLR19, GHZ19b, JLX23, LM24] established before for regular/MHR distributions now can be generalized, with or even without quantitative losses.

cs.GT↗
arXiv2024

Fourier growth of structured $\mathbb{F}_2$-polynomials and applications

We analyze the Fourier growth, i.e. the $L_1$ Fourier weight at level $k$ (denoted $L_{1,k}$), of various well-studied classes of "structured" $\mathbb{F}_2$-polynomials. This study is motivated by applications in pseudorandomness, in particular recent results and conjectures due to [CHHL19,CHLT19,CGLSS20] which show that upper bounds on Fourier growth (even at level $k=2$) give unconditional pseudorandom generators. Our main structural results on Fourier growth are as follows: - We show that any symmetric degree-$d$ $\mathbb{F}_2$-polynomial $p$ has $L_{1,k}(p) \le \Pr[p=1] \cdot O(d)^k$, and this is tight for any constant $k$. This quadratically strengthens an earlier bound that was implicit in [RSV13]. - We show that any read-$Δ$ degree-$d$ $\mathbb{F}_2$-polynomial $p$ has $L_{1,k}(p) \le \Pr[p=1] \cdot (k Δd)^{O(k)}$. - We establish a composition theorem which gives $L_{1,k}$ bounds on disjoint compositions of functions that are closed under restrictions and admit $L_{1,k}$ bounds. Finally, we apply the above structural results to obtain new unconditional pseudorandom generators and new correlation bounds for various classes of $\mathbb{F}_2$-polynomials.

cs.CC↗
arXiv2023

Subset Sum in Time $2^{n/2} / poly(n)$

A major goal in the area of exact exponential algorithms is to give an algorithm for the (worst-case) $n$-input Subset Sum problem that runs in time $2^{(1/2 - c)n}$ for some constant $c>0$. In this paper we give a Subset Sum algorithm with worst-case running time $O(2^{n/2} \cdot n^{-γ})$ for a constant $γ> 0.5023$ in standard word RAM or circuit RAM models. To the best of our knowledge, this is the first improvement on the classical ``meet-in-the-middle'' algorithm for worst-case Subset Sum, due to Horowitz and Sahni, which can be implemented in time $O(2^{n/2})$ in these memory models. Our algorithm combines a number of different techniques, including the ``representation method'' introduced by Howgrave-Graham and Joux and subsequent adaptations of the method in Austrin, Kaski, Koivisto, and Nederlof, and Nederlof and Wegrzycki, and ``bit-packing'' techniques used in the work of Baran, Demaine, and Patrascu on subquadratic algorithms for 3SUM.

cs.DS↗
arXiv2022

Learning Reserve Prices in Second-Price Auctions

This paper proves the tight sample complexity of {\sf Second-Price Auction with Anonymous Reserve}, up to a logarithmic factor, for each of all the value distribution families studied in the literature: $[0,\, 1]$-bounded, $[1,\, H]$-bounded, regular, and monotone hazard rate (MHR). Remarkably, the setting-specific tight sample complexity $\mathsf{poly}(\varepsilon^{-1})$ depends on the precision $\varepsilon \in (0, 1)$, but not on the number of bidders $n \geq 1$. Further, in the two bounded-support settings, our learning algorithm allows {\em correlated} value distributions. In contrast, the tight sample complexity $\tildeΘ(n) \cdot \mathsf{poly}(\varepsilon^{-1})$ of {\sf Myerson Auction} proved by Guo, Huang and Zhang (STOC~2019) has a nearly-linear dependence on $n \geq 1$, and holds only for {\em independent} value distributions in every setting. We follow a similar framework as the Guo-Huang-Zhang work, but replace their information theoretical arguments with a direct proof.

cs.GT↗
arXiv2022

Super-resolution and Robust Sparse Continuous Fourier Transform in Any Constant Dimension: Nearly Linear Time and Sample Complexity

The ability to resolve detail in the object that is being imaged, named by resolution, is the core parameter of an imaging system. Super-resolution is a class of techniques that can enhance the resolution of an imaging system and even transcend the diffraction limit of systems. Despite huge success in the application, super-resolution is not well understood on the theoretical side, especially for any dimension $d \geq 2$. In particular, in order to recover a $k$-sparse signal, all previous results suffer from either/both poly$(k)$ samples or running time. We design robust algorithms for any (constant) dimension under a strong noise model based on developing some new techniques in Sparse Fourier transform (Sparse FT), such as inverting a robust linear system, "eggshell" sampling schemes, and partition and voting methods in high dimension. These algorithms are the first to achieve running time and sample complexity (nearly) linear in the number of source points and logarithmic in bandwidth for any constant dimension, and we believe the techniques developed in the work can find their further applications on the Super-resolution and Sparse FT problem.

cs.DS↗
arXiv2022

Tight Revenue Gaps among Multi-Unit Mechanisms

This paper considers Bayesian revenue maximization in the $k$-unit setting, where a monopolist seller has $k$ copies of an indivisible item and faces $n$ unit-demand buyers (whose value distributions can be non-identical). Four basic mechanisms among others have been widely employed in practice and widely studied in the literature: {\sf Myerson Auction}, {\sf Sequential Posted-Pricing}, {\sf $(k + 1)$-th Price Auction with Anonymous Reserve}, and {\sf Anonymous Pricing}. Regarding a pair of mechanisms, we investigate the largest possible ratio between the two revenues (a.k.a.\ the revenue gap), over all possible value distributions of the buyers. Divide these four mechanisms into two groups: (i)~the discriminating mechanism group, {\sf Myerson Auction} and {\sf Sequential Posted-Pricing}, and (ii)~the anonymous mechanism group, {\sf Anonymous Reserve} and {\sf Anonymous Pricing}. Within one group, the involved two mechanisms have an asymptotically tight revenue gap of $1 + Θ(1 / \sqrt{k})$. In contrast, any two mechanisms from the different groups have an asymptotically tight revenue gap of $Θ(\log k)$.

cs.GT↗
arXiv2022

The Price of Stability for First Price Auction

This paper establishes the Price of Stability (PoS) for First Price Auctions, for all equilibrium concepts that have been studied in the literature: Bayes Nash Equilibrium $\subsetneq$ Bayes Correlated Equilibrium $\subsetneq$ Bayes Coarse Correlated Equilibrium} $\bullet$ Bayes Nash Equilibrium: For independent valuations, the tight PoS is $1 - 1/ e^{2} \approx 0.8647$, matching the counterpart Price of Anarchy (PoA) bound \cite{JL22}. For correlated valuations, the tight $\PoS$ is $1 - 1 / e \approx 0.6321$, matching the counterpart PoA bound \cite{ST13,S14}. This result indicates that, in the worst cases, efficiency degradation depends not on different selections among Bayes Nash Equilibria. $\bullet$ Bayesian Coarse Correlated Equilibrium: For independent or correlated valuations, the tight PoS is always $1 = 100\%$, i.e., no efficiency degradation, different from the counterpart PoA bound $1 - 1 / e \approx 0.6321$ \cite{ST13,S14}. This result indicates that First Price Auctions can be fully efficient when we allow the more general equilibrium concepts.

cs.GT↗
arXiv2021

Average-Case Subset Balancing Problems

Given a set of $n$ input integers, the Equal Subset Sum problem asks us to find two distinct subsets with the same sum. In this paper we present an algorithm that runs in time $O^*(3^{0.387n})$ in the~average case, significantly improving over the $O^*(3^{0.488n})$ running time of the best known worst-case algorithm and the Meet-in-the-Middle benchmark of $O^*(3^{0.5n})$. Our algorithm generalizes to a number of related problems, such as the ``Generalized Equal Subset Sum'' problem, which asks us to assign a coefficient $c_i$ from a set $C$ to each input number $x_i$ such that $\sum_{i} c_i x_i = 0$. Our algorithm for the average-case version of this problem runs in~time $|C|^{(0.5-c_0/|C|)n}$ for some positive constant $c_0$, whenever $C=\{0, \pm 1, \dots, \pm d\}$ or $\{\pm 1, \dots, \pm d\}$ for some positive integer $d$ (with $O^*(|C|^{0.45n})$ when $|C|<10$). Our results extend to the~problem of finding ``nearly balanced'' solutions in which the target is a not-too-large nonzero offset $τ$. Our approach relies on new structural results that characterize the probability that $\sum_{i} c_i x_i$ $=τ$ has a solution $c \in C^n$ when $x_i$'s are chosen randomly; these results may be of independent interest. Our algorithm is inspired by the ``representation technique'' introduced by Howgrave-Graham and Joux. This requires several new ideas to overcome preprocessing hurdles that arise in the representation framework, as well as a novel application of dynamic programming in the solution recovery phase of the algorithm.

cs.CC↗
arXiv2020

Optimal Budget-Feasible Mechanisms for Additive Valuations

In this paper, we show a tight approximation guarantee for budget-feasible mechanisms with an additive buyer. We propose a new simple randomized mechanism with approximation ratio of $2$, improving the previous best known result of $3$. Our bound is tight with respect to either the optimal offline benchmark, or its fractional relaxation. We also present a simple deterministic mechanism with the tight approximation guarantee of $3$ against the fractional optimum, improving the best known result of $(2+ \sqrt{2})$ for the weaker integral benchmark.

cs.GT↗