arXiv subjects

Minji Yang

Publications and source records attributed to Minji Yang.

6 recordsLinked to original sources

arXiv2026

Competitive Equilibrium for Linear Chores is CLS-complete

The competitive equilibrium (CE) is a fundamental concept for markets, with applications to efficient and fair allocation of resources. We consider the fundamental question of computing a CE in the most basic Fisher market model where agents have linear preferences. While it is known that we can compute a CE in strongly polynomial time with linear goods, there is no known polynomial-time algorithm for CE with linear chores. Computing a CE for linear chores is known to be in CLS with no hardness results. In this paper, we prove that computing an exact CE in Fisher markets with divisible chores and linear disutilities is CLS-hard and thus CLS-complete. To the best of our knowledge, this is the first CLS-completeness result for a market equilibrium problem. On the technical side, we use the nonconvex dual Eisenberg-Gale (EG) program whose Karush-Kuhn-Tucker (KKT) points are CE [Chaudhury, Kroer, Mehta, and Nan, 2024], and the CLS-complete problem of computing a KKT point of a quadratic program [Fearnley, Goldberg, Hollender, and Savani, 2024]. We show that from any exact equilibrium of the constructed market, we can recover in polynomial time an $\varepsilon$-KKT point of the input quadratic program over the unit box.

cs.GT↗

arXiv2026

Deterministic Approximation of the Total Variation Distance Between Spin Systems

We study deterministic relative approximation of the total variation distance between two Gibbs distributions induced by spin systems on the same bounded-degree graph. For the hard-core model, we give a deterministic polynomial-time $\varepsilon$-relative-error approximation when both external-field vectors lie in $[b,(1-η)λ_{\mathrm c}(Δ)]^V$, where $b>0$ and $η\in(0,1)$ are fixed and $λ_{\mathrm c}(Δ)$ is the hard-core uniqueness threshold. For the Ising model, we obtain deterministic polynomial-time algorithms in two settings: the ferromagnetic Lee--Yang regime and the antiferromagnetic correlation-decay regime. We develop a new deterministic framework that reduces this task to estimating suitably chosen partition functions.

cs.DS↗

arXiv2026

Rapid mixing in positively weighted restricted Boltzmann machines

We show polylogarithmic mixing time bounds for the alternating-scan sampler for positively weighted restricted Boltzmann machines. This is done via analysing the same chain and the Glauber dynamics for ferromagnetic two-spin systems, where we obtain new mixing time bounds up to the critical thresholds.

cs.DS↗

arXiv2026

On Computing Total Variation Distance Between Mixtures of Product Distributions

We study the problem of approximating the total variation distance between two mixtures of product distributions over an $n$-dimensional discrete domain. Given two mixtures $\mathbb{P}$ and $\mathbb{Q}$ with $k_1$ and $k_2$ product distributions over $[q]^n$, respectively, we give a randomized algorithm that approximates $d_{\mathrm{TV}}\left({\mathbb{P}},{\mathbb{Q}}\right)$ within a multiplicative error of $(1\pm \varepsilon)$ in time $\mathrm{poly}((nq)^{k_1+k_2},1/\varepsilon)$. We also study the special case of mixtures of Boolean subcubes over $\{0,1\}^n$. For this class, we give a deterministic algorithm that exactly computes the total variation distance in time $\mathrm{poly}(n,2^{O(k_1+k_2)})$, and show that exact computation is $\#\mathsf{P}$-hard when $k_1+k_2=Θ(n)$.

cs.DS↗

arXiv2025

Rapid Mixing of Glauber Dynamics for Monotone Systems via Entropic Independence

We study the mixing time of Glauber dynamics on monotone systems. For monotone systems satisfying the entropic independence condition, we prove a new mixing time comparison result for Glauber dynamics. For concrete applications, we obtain $\tilde{O}(n)$ mixing time for the random cluster model induced by the ferromagnetic Ising model with consistently biased external fields, and $\tilde{O}(n^2)$ mixing time for the bipartite hardcore model under the one-sided uniqueness condition, where $n$ is the number of variables in corresponding models, improving the best known results in [Chen and Zhang, SODA'23] and [Chen, Liu, and Yin, FOCS'23], respectively. Our proof combines ideas from the stochastic dominance argument in the classical censoring inequality and the recently developed high-dimensional expanders. The key step in the proof is a novel comparison result between the Glauber dynamics and the field dynamics for monotone systems.

cs.DM↗

arXiv2025

Approximating the total variation distance between spin systems

Spin systems form an important class of undirected graphical models. For two Gibbs distributions $μ$ and $ν$ induced by two spin systems on the same graph $G = (V, E)$, we study the problem of approximating the total variation distance $d_{TV}(μ,ν)$ with an $ε$-relative error. We propose a new reduction that connects the problem of approximating the TV-distance to sampling and approximate counting. Our applications include the hardcore model and the antiferromagnetic Ising model in the uniqueness regime, the ferromagnetic Ising model, and the general Ising model satisfying the spectral condition. Additionally, we explore the computational complexity of approximating the total variation distance $d_{TV}(μ_S,ν_S)$ between two marginal distributions on an arbitrary subset $S \subseteq V$. We prove that this problem remains hard even when both $μ$ and $ν$ admit polynomial-time sampling and approximate counting algorithms.

cs.DS↗