arXiv subjects

Zihe Wang

Publications and source records attributed to Zihe Wang.

At least 19 recordsLinked to original sources

arXiv2026

Constant Approximation of Fréchet Distance in Near-Linear Time

We give the first constant-factor approximation for the Fréchet distance in near-linear time. Given two polygonal curves in $\mathbb{R}^d$ with $n$ and $m$ vertices, respectively, where $m\le n$, our deterministic algorithm runs in $O(n^{1+\varepsilon})$ time for every fixed $\varepsilon>0$ and $d$, with an approximation factor depending only on $\varepsilon$ and $d$. The same result holds for the discrete Fréchet distance. Our result extends the line of work initiated by Cheng, Huang, and Zhang (STOC 2025) from strongly subquadratic to near-linear time. Our algorithm recursively balances preprocessing and query time. An index for comparing subcurves of a single curve supports faster queries between different curves. We obtain this speedup by replacing one curve with surrogates assembled from indexed subcurves of the other and shared across starting points of matchings. Faster queries then reduce the cost of building the next index. Compact boundary reachability summaries allow the answers to be reused in later recursive calls. After a number of rounds depending only on $\varepsilon$, both preprocessing and query time are near-linear.

cs.CG↗

arXiv2026

Cold-Start Pricing of LLM Services under Two-Sided Learning

Online large language model (LLM) services face a pricing cold start: providers initially lack the historical data and user information needed for precise pricing, while users' willingness to pay evolves with repeated use. We formulate this challenge as a \emph{two-sided learning} problem between a provider and a user. The user learns from private usage experience, whereas the provider incurs a serving cost and dynamically adapts prices using only purchase decisions to maximize cumulative profit. The provider's central challenge is to learn to price against an evolving willingness to pay without observing the private experiences driving that evolution. We establish matching upper and lower bounds on the minimax regret over horizon $T$, identifying two cost-dependent regimes. When serving costs are sufficiently low, our Calibration-and-Tracking (CAT) algorithm achieves the optimal rate $Θ(T^{1/3})$. In the higher-cost regime, where the provider must learn whether continued service is profitable, Calibration-and-Tracking with Retirement (CAT-R) attains the optimal rate $Θ(\sqrt{T})$. This phase transition shows that serving costs affect not only profit margins but also the fundamental difficulty of learning to price LLM services. Simulations support the predicted regret scaling and show that our algorithms outperform standard online learning baselines in the evaluated settings.

cs.GT↗

arXiv2026

Finite-Size Limits of Adaptive Pauli Prediction

The expectation values of a predetermined set of Pauli observables can be predicted using only a few copies of a quantum state. However, when later observables depend on earlier predictions, how the system size constrains the required number of copies remains unclear. We use classical interactive fingerprinting codes to establish this constraint. A compact Pauli-parity encoding embeds the fingerprinting interaction into the quantum prediction task, allowing any quantum prediction mechanism on the constructed diagonal states to be simulated by a classical response strategy subject to the same information constraints. We show that accurate prediction from too few copies would violate the guarantees of the fingerprinting code. For $n$ qubits and $M$ adaptively chosen Pauli observables, requiring all predictions to be simultaneously accurate to a fixed additive error with probability at least $2/3$ yields the worst-case lower bound $N^*(n,M)=Ω(\sqrt{\min\{n,M\}})$ on the required number of copies. For $M\le n$, this lower bound matches known upper bounds. In particular, $n$ adaptive predictions require $Θ(\sqrt{n})$ copies, whereas the same number of predetermined queries requires only $O(\log n)$ copies. This separation persists even for diagonal states and commuting observables.

quant-ph↗

arXiv2026

Pricing Information in Search with Nonobligatory Inspection

As AI agents reshape Web search and advertising, platforms can monetize information that improves decisions. We study information pricing for sequential search among independent alternatives with nonobligatory inspection: the buyer may select any alternative without buying its report. We show that a common fee maximizes static revenue for identical priors, resolving a uniform-pricing conjecture. Our results also establish that exact optimization is NP-hard for heterogeneous binary priors. Despite this hardness, our polynomial-time static pricing algorithm achieves a $3$-approximation to the information surplus. More generally, a common static fee approximates optimal adaptive revenue within a logarithmic factor in the number of alternatives. This guarantee is asymptotically tight.

cs.GT↗

arXiv2026

GSP Autobidding Equilibria with Few Advertisers or Slots

In sponsored-shopping auctions, one advertiser may win several positions, and a product that is never displayed may determine the prices of several winners. Under generalized second-price (GSP) pricing without self-pricing, these interactions couple allocation and payment through a single global ranking. We prove that exact autobidding equilibria under budget and return-on-investment (ROI) constraints can be computed in polynomial time whenever either the number $n$ of advertisers or the number $K$ of display slots is fixed. Our algorithms rely on two structural reductions. With few advertisers, the payment polytopes of tied bid layers combine by a Minkowski sum, giving a fixed-dimensional representation of exponentially many rankings. With few slots, budget equilibria admit threshold recovery and an exact submodular description of attainable payments at the display boundary. For ROI, we prove that every group-consecutive equilibrium has a representative with at most $K+2$ nonunit multipliers, preserving the item and price in every displayed slot. In each case, the reduction leads to polynomially many systems of polynomial equations and inequalities in bounded dimension. The algorithms compute exact multipliers and explicit distributions over valid group-consecutive rankings, with support at most $n+1$; for ROI with few slots, this improves to $\min\{n+1,K+3\}$.

cs.GT↗

arXiv2026

Hardness Amplification for Approximate Nash Equilibrium with Constantly Many Players

For every fixed $\varepsilon\in(0,1)$ and $η\in[0,1)$, we prove that computing an $(\varepsilon,η)$-weak approximate Nash equilibrium requires quasipolynomial time assuming deterministic PPAD-ETH, even in symmetric binary-payoff games with a constant number of players. The games are given by complete payoff tables, and the player count depends only on the tolerances. The weak approximate Nash equilibrium allows at most an $η$ fraction of players to gain more than $\varepsilon$ by deviating unilaterally. The main technical result is an unconditional error-amplification reduction from bimatrix games. For every fixed $δ\in(0,1)$, it transforms a rational bimatrix game with payoffs in $[0,1]$ into a symmetric binary-payoff game with a polynomial-size complete table and a player count depending only on $δ,\varepsilon,η$. Every $(\varepsilon,η)$-weak approximate equilibrium of the constructed game yields a $δ$-approximate Nash equilibrium of the bimatrix game. Construction and recovery take polynomial time in their explicit inputs. Combining this reduction with the bimatrix hardness result of Rubinstein [FOCS 16] gives a deterministic worst-case running-time lower bound of $N^{(\log N)^{1-o(1)}}$, where $N$ is the constructed table's binary encoding length.

cs.GT↗

arXiv2026

Optimal Multi-Item Auctions with I.I.D. Values

We study revenue-maximizing multi-item auctions under dominant-strategy incentive compatibility (DSIC) and ex-post individual rationality. Buyers have additive valuations, and all item values are independent draws from a common finite distribution. For every two-point distribution and arbitrary numbers of buyers and items, we give an explicit deterministic mechanism that is optimal among all randomized mechanisms satisfying these requirements, together with a polynomial-time algorithm for computing the optimal expected revenue. For general finite-support distributions, computing the exact optimal revenue is $\#\mathrm P$-hard, both for a single buyer with an arbitrary number of items and for two items with an arbitrary number of buyers. For a single buyer, we also establish hardness of computing an optimal mechanism. Building on prior work, we also obtain exact and approximate algorithms under different parameter restrictions. Exact polynomial-time optimization is possible whenever any two of the buyer count, item count, and support size are fixed. When only the item count is fixed, a polynomial-time approximation scheme constructs a mechanism with expected revenue at least a $1-\varepsilon$ fraction of the optimum for every fixed $0<\varepsilon<1$. All these algorithms satisfy DSIC and ex-post individual rationality.

cs.GT↗

arXiv2026

Dimension Amplification for Tarski Fixed-Point Query Lower Bounds

We prove that finding a fixed point of a monotone map on the nine-dimensional grid $[N]^9$ requires $Ω((\log N)^3)$ deterministic queries, even when the fixed point is unique and each query returns the entire function value. The proof gives a construction that raises the dimension from $d$ to $4d+1$, preserves uniqueness, and adds a logarithmic factor to the lower bound. Iteration gives $Ω((\log N)^{r+2})$ queries in dimension $(7\cdot4^r-1)/3$, for every fixed nonnegative integer $r$, with an implicit constant that may depend on $r$. Consequently, no finite logarithmic exponent bounds the query complexity in all fixed dimensions.

cs.CC↗

arXiv2026

Sharp Second-Best Welfare in Bilateral and Matching Markets

How much social welfare must a market lose because values are private? We determine the sharp ratio of second-best to first-best welfare under independent nonnegative types, Bayesian incentive compatibility, interim individual rationality, and no expected budget deficit. The ratio is approximately $0.8882516903$ for arbitrary priors and $0.9113893681$ when buyers have monotone hazard rates and sellers are unrestricted. The arbitrary-prior guarantee holds for every downward-closed family of feasible matchings; the MHR guarantee holds when every matching of a compatibility graph is feasible. Both constants are \revise{attained}{sharp} already in bilateral trade. The proof keeps the sellers' initial endowment inside the budget Lagrangian. For arbitrary priors, a common threshold decomposition reduces the problem to three-parameter power-law distributions. For monotone hazards, common transformations of buyer and seller scores reduce it to shifted capped exponential buyers; a typewise allocation certificate and an explicit worst-case seller satisfy the same boundary equation. The bilateral-to-matching framework, with a welfare endowment charge and an MHR-preserving packing argument, transfers these affine inequalities without loss. We give exact variational characterizations of both constants and reproducible interval certificates for their numerical evaluation. Unrestricted signed transfers also permit pointwise strong budget balance.

cs.GT↗

arXiv2026

From Bilateral Trade to Matching Markets: Sharp Gains from Trade

We study gains from trade in matching markets with independent private values and costs, Bayesian incentive compatibility, interim individual rationality, and no expected budget deficit. A second-best guarantee for finite bilateral trade extends without loss to matching markets with independent Borel priors, arbitrary downward-closed feasibility, and finite expected first-best gains. For bounded buyers with monotone hazard rates and arbitrary bounded sellers, we determine the exact worst-case ratio of second-best to first-best gains, approximately $0.72490721$. For binary buyers and sellers with at most $m$ types, we determine the exact ratio for every $m$, including $8/9$ when $m=2$ and a limit of $4/5$ as $m$ grows. Both families of bounds are tight already in bilateral trade.

cs.GT↗

arXiv2026

Random Forest-Based Prediction of Bone Volume Fraction and Fracture Position from S-Parameters

In this paper, we propose a method for predicting bone volume fraction (BVF) and fracture position by constructing a random forest model based on multichannel S-parameters. A nine-antenna microwave scanning system is designed and fabricated to acquire the multichannel S-parameter data. Bone-mimicking phantoms are developed, and corresponding experiments are conducted to validate the effectiveness of the proposed approach. Both synthetic and experimental results demonstrate the validity of the method.

cs.LG↗

arXiv2026

Private Private Information in Second-Price Auction

Classic results show that even an arbitrarily small correlation across bidders' information can enable full surplus extraction in auctions and related mechanism design settings. Motivated by this fragility, we study the information independence in a second-price auction when the seller commits to a private private information structure, meaning bidders' signals are independent ex ante, while bidders share a symmetric and arbitrarily correlated prior distribution over their valuations. We first show that the seller optimal efficient outcome with full surplus extraction can always be implemented by a private private information structure that admits a Bayes Nash equilibrium. However, this equilibrium may not be stable. We then further construct a private private information structure that achieves revenue arbitrarily close to maximum welfare while admitting a strict equilibrium. At the same time, we establish an impossibility result: under private private information, in general, bidder surplus cannot achieve maximal welfare exactly, and we characterize necessary and sufficient conditions on the prior distribution under which bidder surplus can be made arbitrarily close to maximal welfare. We finally explore which other efficient outcomes are achievable under private private information.

econ.TH↗

arXiv2026

Algorithmic Information Design for Searchers with Uncertain Alternatives

Advertisements reveal information to consumers who decide on further information acquisition and eventual purchase. Anderson and Renault (2006) first modeled this problem using an information-design framework where the advertiser acts as a sender and the consumer as a receiver. Due to search frictions and the consumer's outside option, search for additional information is not always worthwhile for the receiver. Thus, the sender's information design is used to make further search attractive and ultimately induce purchase. Following Lyu (2023), we study the optimal information design for a sender who sells search goods to a consumer with uncertain alternatives. Instead of making relaxations to the sender's problem (as done in Lyu, 2023), we work directly on the joint distribution over realized values and signals. Our contributions are twofold. First, we give a method, based on duality arguments, to verify whether a given information strategy is optimal. We illustrate the value of this verification framework in a competitive extension, where it certifies a non-trivial symmetric equilibrium for two senders with a common convex prior. Second, on the algorithmic front, we develop an FPTAS that finds for the seller a signaling scheme whose utility differs from that of the optimal solution by at most an additive $ε$ error, for any $ε> 0$.

cs.GT↗

arXiv2026

Second-Best Bilateral Trade is $1/2$ Efficient

The landmark Myerson-Satterthwaite Theorem establishes a fundamental impossibility in bilateral trade: no Bayesian incentive-compatible mechanism can simultaneously achieve ex-post efficiency, individual rationality, and strong budget balance. We resolve a long-standing open question regarding the efficiency loss imposed by these constraints. Specifically, we prove that the Bayesian-optimal (second-best) mechanism always captures at least half of the first-best gains from trade ($\mathrm{SB}\ge\frac{1}{2}\mathrm{FB}$). This result is tight, definitively closing the gap between the previously best-known bounds of $0.317$ and $0.736$.

cs.GT↗

arXiv2026

Pacing Equilibria in Second-Price Auctions with Few Goods

In this paper, we investigate the computation of second-price pacing equilibria (SPPEs), a foundational model in online advertising auctions. We present a polynomial-time algorithm for computing exact SPPEs in instances with a constant number of goods. Our core technique maps buyers' pacing multipliers to the highest bids on each good, effectively partitioning the parameter space into a set of distinct geometric cells. By enumerating these cells, we fix the relative ordering of the bids and reduce the problem of equilibrium computation to a linear feasibility program. Finally, we demonstrate that this tractability extends to large-scale markets with an arbitrary number of goods, provided the goods can be aggregated into a constant number of valuation types.

cs.GT↗

arXiv2026

AVA-Bench: Atomic Visual Ability Benchmark for Vision Foundation Models

The rise of vision foundation models (VFMs) calls for systematic evaluation. A common approach pairs VFMs with large language models (LLMs) as general-purpose heads, followed by evaluation on broad Visual Question Answering (VQA) benchmarks. However, this protocol has two key blind spots: (i) the instruction tuning data may not align with VQA test distributions, meaning a wrong prediction can stem from such data mismatch rather than a VFM' visual shortcomings; (ii) VQA benchmarks often require multiple visual abilities, making it hard to tell whether errors stem from lacking all required abilities or just a single critical one. To address these gaps, we introduce AVA-Bench, the first benchmark that explicitly disentangles 14 Atomic Visual Abilities (AVAs) -- foundational skills like localization, depth estimation, and spatial understanding that collectively support complex visual reasoning tasks. By decoupling AVAs and matching training and test distributions within each, AVA-Bench pinpoints exactly where a VFM excels or falters. Applying AVA-Bench to leading VFMs thus reveals distinctive "ability fingerprints," turning VFM selection from educated guesswork into principled engineering. Notably, we find that a 0.5B LLM yields similar VFM rankings as a 7B LLM while cutting GPU hours by 8x, enabling more efficient evaluation. By offering a comprehensive and transparent benchmark, we hope AVA-Bench lays the foundation for the next generation of VFMs.

cs.CV↗

arXiv2026

ExpressMind: A Multimodal Pretrained Large Language Model for Expressway Operation

The current expressway operation relies on rule-based and isolated models, which limits the ability to jointly analyze knowledge across different systems. Meanwhile, Large Language Models (LLMs) are increasingly applied in intelligent transportation, advancing traffic models from algorithmic to cognitive intelligence. However, general LLMs are unable to effectively understand the regulations and causal relationships of events in unconventional scenarios in the expressway field. Therefore, this paper constructs a pre-trained multimodal large language model (MLLM) for expressways, ExpressMind, which serves as the cognitive core for intelligent expressway operations. This paper constructs the industry's first full-stack expressway dataset, encompassing traffic knowledge texts, emergency reasoning chains, and annotated video events to overcome data scarcity. This paper proposes a dual-layer LLM pre-training paradigm based on self-supervised training and unsupervised learning. Additionally, this study introduces a Graph-Augmented RAG framework to dynamically index the expressway knowledge base. To enhance reasoning for expressway incident response strategies, we develop a RL-aligned Chain-of-Thought (RL-CoT) mechanism that enforces consistency between model reasoning and expert problem-solving heuristics for incident handling. Finally, ExpressMind integrates a cross-modal encoder to align the dynamic feature sequences under the visual and textual channels, enabling it to understand traffic scenes in both video and image modalities. Extensive experiments on our newly released multi-modal expressway benchmark demonstrate that ExpressMind comprehensively outperforms existing baselines in event detection, safety response generation, and complex traffic analysis. The code and data are available at: https://wanderhee.github.io/ExpressMind/.

cs.AI↗

arXiv2026

Mechanism Design via Market Clearing-Prices for Value Maximizers under Budget and RoS Constraints

The transition to auto-bidding in online advertising has shifted the focus of auction theory from quasi-linear utility maximization to value maximization subject to financial constraints. We study mechanism design for buyers with private budgets and private Return-on-Spend (RoS) constraints, but public valuations, a setting motivated by modern advertising platforms where valuations are predicted via machine learning models. We introduce the extended Eisenberg-Gale program, a convex optimization framework generalized to incorporate RoS constraints. We demonstrate that the solution to this program is unique and characterizes the market's competitive equilibrium. Based on this theoretical analysis, we design a market-clearing mechanism and prove two key properties: (1) it is incentive-compatible with respect to financial constraints, making truthful reporting the optimal strategy; and (2) it achieves a tight 1/2-approximation of the first-best revenue benchmark, the maximum revenue of any feasible mechanism, regardless of IC. Finally, to enable practical implementation, we present a decentralized online algorithm. Ignoring logarithmic factors, we prove that under this algorithm, both the seller's revenue and each buyer's utility converge to the equilibrium benchmarks with a sublinear regret of $\tilde{O}(\sqrt{m})$ over $m$ auctions.

cs.GT↗