arXiv subjects

Shixin Wang

Publications and source records attributed to Shixin Wang.

13 recordsLinked to original sources

arXiv2026

Perfect state transfer on Cayley graphs over dihedral groups: A complete and practical characterization

Perfect state transfer on graphs has attracted extensive attention due to its application in quantum information and quantum computation. Explicit characterizations of connection sets admitting perfect state transfer in Cayley graphs are rare and, so far, are known only for a few abelian Cayley graphs. In this paper, we characterize the conjugation-closed connection sets of connected Cayley graphs over dihedral groups that admit perfect state transfer. By applying Ramanujan sums, M\"obius inversion, and arguments based on the $p$-adic exponential valuation of rational numbers, we convert the eigenvalue constraints imposed by perfect state transfer into explicit structural conditions on the connection set. This yields a complete and practical characterization, which gives an effective criterion for recognizing and constructing such Cayley graphs and also determines the exact minimum perfect state transfer time.

math.CO↗

arXiv2026

Online Bipartite Matching with Reusable Capacity under Non-Stationary Rewards

We study online bipartite matching with reusable server capacity and non-stationary rewards. Jobs arrive sequentially, reveal compatible servers, reward rates, and processing durations, and must be accepted or rejected irrevocably. An accepted job occupies one unit of server capacity only during its processing interval, so an assignment may displace an unknown sequence of future jobs. Existing guarantees are typically calibrated by a global reward range, which can become arbitrarily large when rewards drift over a long horizon. We instead impose a locally bounded reward condition: reward rates of jobs that can compete for the same server within a relevant time window differ by at most a factor $\delta$. Under this condition, we develop two BALANCE-type algorithms with time-aware opportunity-cost losses. TS-BAL maximizes cumulative blocking losses over feasible reuse schedules and achieves a competitive ratio of $2\ln(\delta D)+\mathcal O(\ln\ln(\delta\vee D))$. GR-BAL uses a greedy relaxation of this loss and achieves $\ln(\delta D)+\mathcal O(\ln\ln(\delta\vee D))$, matching a lower bound of $\ln(\delta D)$ in the leading term. Numerical experiments demonstrate robust performance under substantial global reward drift and favorable finite-capacity performance.

math.OC↗

arXiv2026

Optimal Pricing with Unreliable Signals

We study a single-buyer pricing problem with unreliable side information, motivated by the increasing use of AI-assisted decision-making and LLM-based predictions. The seller observes a private sample that may be either accurate (coinciding with the buyer's valuation), or hallucinatory (an independent draw from the prior), without knowing which case has realized. The buyer does not observe the realized signal, yet knows whether it is accurate or hallucinatory. This creates a higher-order informational asymmetry: the seller is uncertain about the reliability of his own side information, while the buyer has private information about that reliability. Adopting a consistency-robustness framework, we characterize the exact Pareto frontier of tradeoffs between consistency (performance under an accurate signal) and robustness (performance under a hallucinatory signal). We show that keeping the unreliable signal private generates substantial value, yielding tradeoffs that strictly dominate any public-signal benchmark. We further show that perfect consistency does not preclude meaningful protection against hallucination: for every prior, there exists a mechanism achieving perfect consistency together with a nontrivial robustness guarantee of $\frac{1}{2}$. Moreover, if the prior has an infinite mean or a mean of at most its monopoly price, we provide a mechanism that is simultaneously 1-consistent and 1-robust. Our results illustrate a new mechanism design paradigm: rather than relying only on information directly possessed by the designer, mechanisms can be built to leverage the other side's knowledge about the reliability of the designer's information.

cs.GT↗

arXiv2026

Robust Mechanism Design with Anonymous Information

In practice, auction data are often endogenously censored and anonymous, revealing only limited outcome statistics rather than full bid profiles. We study robust auction design when the seller observes only aggregated, anonymous order statistics and seeks to maximize worst-case expected revenue over all product distributions consistent with the observed statistic. We show that simple and widely used mechanisms are robustly optimal. Specifically, posted pricing is robustly optimal given the distribution of the highest value; the Myerson auction designed for the unique consistent i.i.d. distribution is robustly optimal given the lowest value distribution; and the second-price auction with an optimal reserve is robustly optimal when an intermediate order statistic is observed and the implied i.i.d. distribution is regular above its reserve. More generally, for a broad class of monotone symmetric mechanisms depending only on the top k order statistics, including multi-unit and position auctions, the worst-case revenue is attained under the i.i.d. distribution consistent with the observed k-th order statistic. Our results provide a tractable foundation for non-discriminatory auction design, where fairness and privacy are intrinsic consequences of the information structure rather than imposed constraints.

econ.TH↗

arXiv2026

Pricing with a Hidden Sample

We study prior-independent pricing for selling a single item to a single buyer when the seller observes only a single sample from the valuation distribution, while the buyer knows the distribution. Classical robust pricing approaches either rely on distributional statistics, which typically require many samples to estimate, or directly use revealed samples to determine prices and allocations. We show that these two regimes can be bridged by leveraging the buyer's informational advantage: pricing policies that conventionally require the seller to know statistics such as the mean, $L^\eta$-norm, or superquantile can, in our framework, be implemented using only a single hidden sample. We introduce hidden pricing mechanisms, in which the seller commits ex ante to a pricing rule based on a single sample that is revealed only after the buyer's participation decision. We show that every concave pricing policy can be implemented in this way. To evaluate performance guarantees, we develop a general reduction for analyzing monotone pricing policies over $\alpha$-regular distributions, enabling a tractable characterization of worst-case instances. Using this reduction, we characterize the optimal monotone hidden pricing mechanisms and compute their approximation ratios; in particular, we obtain an approximation ratio of approximately $0.79$ for monotone hazard rate (MHR) distributions. We further establish impossibility results for general concave pricing policies and for all prior-independent mechanisms. Finally, we show that our framework also applies to statistic-based robust pricing, thereby unifying sample-based and statistic-based approaches.

cs.GT↗

arXiv2025

Multi-Item Screening with a Maximin-Ratio Objective

In multi-item screening, optimal selling mechanisms are challenging to characterize and implement, even with full knowledge of valuation distributions. In this paper, we aim to develop tractable, interpretable, and implementable mechanisms with strong performance guarantees in the absence of precise distributional knowledge. In particular, we study robust screening with a maximin ratio objective. We show that given the marginal support of valuations, the optimal mechanism is separable: each item's allocation probability and payment depend only on its own valuation and not on other items' valuations. However, we design the allocation and payment rules by leveraging the available joint support information. This enhanced separable mechanism can be efficiently implemented through randomized pricing for individual products, which is easy to interpret and implement. Moreover, our framework extends naturally to scenarios where the seller possesses marginal support information on aggregate valuations for any product bundle partition, for which we characterize a bundle-wise separable mechanism and its guarantee. Beyond rectangular-support ambiguity sets, we further establish the optimality of randomized grand bundling mechanisms within a broad class of ambiguity sets, which we term ``$\boldsymbolρ-$scaled invariant ambiguity set".

econ.TH↗

arXiv2025

On $2$-integral Cayley graphs

In this paper, we introduce the concept of $k$-integral graphs. A graph $Γ$ is called $k$-integral if the extension degree of the splitting field of the characteristic polynomial of $Γ$ over rational field $\mathbb Q$ is equal to $k$. We prove that the set of all finite connected graphs with given algebraic degree and maximum degree is finite. $1$-integral graphs are just integral ones, graphs all of whose eigenvalues are integer. We study $2$-integral Cayley graphs over finite groups $G$ with respect to Cayley sets which are a union of conjugacy classes of $G$. Among other general results, we completely characterize all finite abelian groups having a connected $2$-integral Cayley graph with valency $2,3,4$ and $5$. Furthermore, we classify finite groups $G$ for which all Cayley graphs over $G$ with bounded valency are $2$-integral.

math.CO↗

arXiv2025

Traffic Flow and Speed Monitoring Based On Optical Fiber Distributed Acoustic Sensor

In the realm of intelligent transportation systems, accurate and reliable traffic monitoring is crucial. Traditional devices, such as cameras and lidars, face limitations in adverse weather conditions and complex traffic scenarios, prompting the need for more resilient technologies. Thispaperpresentstrafficflowmonitoringmethodusingopticalfiber-baseddistributedacoustic sensors(DAS).Aninnovativevehicletrajectoryextractionalgorithmisproposedtoderivetraffic flow statistics. In the processing of optical fiber waterfall diagrams, Butterworth low-pass filter and peaks location search algorithm are employed to determine the entry position of vehicles. Subsequently, line-by-line matching algorithm is proposed to effectively track the trajectories. Experiments were conducted in highway, tunnel and city scenarios. Visualizations show that ourapproachnotonlyextractsvehicletrajectoriesmoreaccuratelythantheclassicalHoughand Radon transform-based methods and MUSIC beamforming algorithm, but also facilitates the calculation of traffic flow information using the low-cost acoustic sensors. It provides a new reliable means for traffic flow monitoring which can be integrated with existing methods like vision-based method.

eess.SP↗

arXiv2024

The Power of Simple Menus in Robust Selling Mechanisms

We study a robust selling problem where a seller attempts to sell one item to a buyer but is uncertain about the buyer's valuation distribution. Existing literature shows that robust screening provides a stronger theoretical guarantee than robust deterministic pricing, but at the expense of implementation complexity, as it requires a menu of infinite options. Our research aims to find simple mechanisms to hedge against market ambiguity effectively. We develop a general framework for robust selling mechanisms with a finite menu (or randomization across finite prices). We propose a tractable reformulation that addresses various ambiguity sets of the buyer's valuation distribution, including support, mean, and quantile ambiguity sets. We derive optimal selling mechanisms and corresponding performance ratios for different menu sizes, showing that even a modest menu size can deliver benefits similar to those achieved by the optimal robust mechanism with infinite options, establishing a favorable trade-off between theoretical performance and implementation simplicity. Remarkably, a menu size of merely two can significantly enhance the performance ratio compared to deterministic pricing.

econ.TH↗

arXiv2024

Embedding arbitrary edge-colorings of hypergraphs into regular colorings

For $\textbf{r}=(r_1,\ldots,r_k)$, an $\textbf{r}$-factorization of the complete $λ$-fold $h$-uniform $n$-vertex hypergraph $λK_n^h$ is a partition of the edges of $λK_n^h$ into $F_1,\ldots, F_k$ such that $F_j$ is $r_j$-regular and spanning for $1\leq j\leq k$. This paper shows that for $n>\frac{m-1}{1-2^{\frac{1}{1-h}}}+h-1$, a partial $\textbf{r}$-factorization of $λK_m^h$ can be extended to an $\textbf{r}$-factorization of $λK_n^h$ if and only if the obvious necessary conditions are satisfied.

math.CO↗

arXiv2023

Algebraic degrees of quasi-abelian semi-Cayley digraphs

For a digraph $Γ$, if $F$ is the smallest field that contains all roots of the characteristic polynomial of the adjacency matrix of $Γ$, then $F$ is called the splitting field of $Γ$. The extension degree of $F$ over the field of rational numbers $\mathbb{Q}$ is said to be the algebraic degree of $Γ$. A digraph is a semi-Cayley digraph over a group $G$ if it admits $G$ as a semiregular automorphism group with two orbits of equal size. A semi-Cayley digraph $\mathrm{SC}(G,T_{11},T_{22},T_{12},T_{21})$ is called quasi-abelian if each of $T_{11},T_{22},T_{12}$ and $T_{21}$ is a union of some conjugacy classes of $G$. This paper determines the splitting field and the algebraic degree of a quasi-abelian semi-Cayley digraph over any finite group in terms of irreducible characters of groups. This work generalizes the previous works on algebraic degrees of Cayley graphs over abelian groups and any group having a subgroup of index 2, and semi-Cayley digraphs over abelian groups.

math.CO↗

arXiv2023

Perfect state transfer on bi-Cayley graphs over abelian groups

The study of perfect state transfer on graphs has attracted a great deal of attention during the past ten years because of its applications to quantum information processing and quantum computation. Perfect state transfer is understood to be a rare phenomenon. This paper establishes necessary and sufficient conditions for a bi-Cayley graph having perfect state transfer over any given finite abelian group. As corollaries, many known and new results are obtained on Cayley graphs having perfect state transfer over abelian groups, (generalized) dihedral groups, semi-dihedral groups and generalized quaternion groups. Especially, we give an example of a connected non-normal Cayley graph over a dihedral group having perfect state transfer between two distinct vertices, which was thought impossible.

math.CO↗

arXiv2023

Leveraging Reusability: Improved Competitive Ratio of Greedy for Reusable Resources

We study online weighted bipartite matching of reusable resources where an adversarial sequence of requests for resources arrive over time. A resource that is matched is 'used' for a random duration, drawn independently from a resource-dependent distribution, after which it returns and is able to be matched again. We study the performance of the greedy policy, which matches requests to the resource that yields the highest reward. Previously, it was known that the greedy policy is 1/2 competitive against a clairvoyant benchmark that knows the request sequence in advance. In this work, we improve this result by introducing a parameter that quantifies the degree of reusability of the resources. Specifically, if p represents the smallest probability over the usage distributions that a matched resource returns in one time step, the greedy policy achieves a competitive ratio of $1/(2-p)$. Furthermore, when the usage distributions are geometric, we establish a stronger competitive ratio of $(1+p)/2$, which we demonstrate to be tight. Both of these results align with the known results in the two extreme scenarios: p = 0 corresponds to non-reusable resources, where 1/2 is known to be tight, while p = 1 corresponds to every resource returning immediately, where greedy is the optimal policy and hence the competitive ratio is 1. Finally, we show that both results are robust to approximations of the greedy policy. Our work demonstrates that the reusability of resources can enhance performance compared to the non-reusable setting, and that a simple greedy policy suffices when the degree of reusability is high. Our insights contribute to the understanding of how resource reusability can influence the performance of online algorithms, and highlight the potential for improved performance as the degree of reusability increases.

cs.DS↗