arXiv subjects

Chenghao Guo

Publications and source records attributed to Chenghao Guo.

10 recordsLinked to original sources

arXiv2026

Achievability of Heterogeneous Hypergraph Recovery from its Graph Projection

We formulate and analyze a heterogeneous random hypergraph model, and we provide an achieveability result for recovery of hyperedges from the observed projected graph. We observe a projected graph which combines random hyperedges across all degrees, where a projected edge appears if and only if both vertices appear in at least one hyperedge. Our goal is to reconstruct the original set of hyperedges of degree $d_j$ for some $j$. Our achievability result is based on the idea of selecting maximal cliques of size $d_j$ in the projected graph, and we show that this algorithm succeeds under a natural condition on the densities. This achievability condition generalizes a known threshold for $d$-uniform hypergraphs with noiseless and noisy projections. We conjecture the threshold to be optimal for recovering hyperedges with the largest degree.

cs.DS↗

arXiv2025

Partial and Exact Recovery of a Random Hypergraph from its Graph Projection

Consider a $d$-uniform random hypergraph on $n$ vertices in which hyperedges are included iid so that the average degree is $n^δ$. The projection of a hypergraph is a graph on the same $n$ vertices where an edge connects two vertices if and only if they belong to some hyperedge. The goal is to reconstruct the hypergraph given its projection. An earlier work of Bresler, Guo, and Polyanskiy (COLT 2024) showed that exact recovery for $d=3$ is possible if and only if $δ< 2/5$. This work completely resolves the question for all values of $d$ for both exact and partial recovery and for both cases of whether multiplicity information about each edge is available or not. In addition, we show that the reconstruction fidelity undergoes an all-or-nothing transition at a threshold. In particular, this resolves all conjectures from Bresler, Guo, and Polyanskiy (COLT 2024).

math.CO↗

arXiv2025

Thresholds for Reconstruction of Random Hypergraphs From Graph Projections

The graph projection of a hypergraph is a simple graph with the same vertex set and with an edge between each pair of vertices that appear in a hyperedge. We consider the problem of reconstructing a random $d$-uniform hypergraph from its projection. Feasibility of this task depends on $d$ and the density of hyperedges in the random hypergraph. For $d=3$ we precisely determine the threshold, while for $d\geq 4$ we give bounds. All of our feasibility results are obtained by exhibiting an efficient algorithm for reconstructing the original hypergraph, while infeasibility is information-theoretic. Our results also apply to mildly inhomogeneous random hypergrahps, including hypergraph stochastic block models (HSBM). A consequence of our results is an optimal HSBM recovery algorithm, improving on a result of Guadio and Joshi in 2023.

math.ST↗

arXiv2023

Algorithmic Decorrelation and Planted Clique in Dependent Random Graphs: The Case of Extra Triangles

We aim to understand the extent to which the noise distribution in a planted signal-plus-noise problem impacts its computational complexity. To that end, we consider the planted clique and planted dense subgraph problems, but in a different ambient graph. Instead of Erdős-Rényi $G(n,p)$, which has independent edges, we take the ambient graph to be the random graph with triangles (RGT) obtained by adding triangles to $G(n,p)$. We show that the RGT can be efficiently mapped to the corresponding $G(n,p)$, and moreover, that the planted clique (or dense subgraph) is approximately preserved under this mapping. This constitutes the first average-case reduction transforming dependent noise to independent noise. Together with the easier direction of mapping the ambient graph from Erdős-Rényi to RGT, our results yield a strong equivalence between models. In order to prove our results, we develop a new general framework for reasoning about the validity of average-case reductions based on low sensitivity to perturbations.

math.PR↗

arXiv2023

Smoothed Complexity of SWAP in Local Graph Partitioning

We give the first quasipolynomial upper bound $ϕn^{\text{polylog}(n)}$ for the smoothed complexity of the SWAP algorithm for local Graph Partitioning (also known as Bisection Width), where $n$ is the number of nodes in the graph and $ϕ$ is a parameter that measures the magnitude of perturbations applied on its edge weights. More generally, we show that the same quasipolynomial upper bound holds for the smoothed complexity of the 2-FLIP algorithm for any binary Maximum Constraint Satisfaction Problem, including local Max-Cut, for which similar bounds were only known for $1$-FLIP. Our results are based on an analysis of cycles formed in long sequences of double flips, showing that it is unlikely for every move in a long sequence to incur a positive but small improvement in the cut weight.

cs.DS↗

arXiv2023

Linear Programs with Polynomial Coefficients and Applications to 1D Cellular Automata

Given a matrix $A$ and vector $b$ with polynomial entries in $d$ real variables $δ=(δ_1,\ldots,δ_d)$ we consider the following notion of feasibility: the pair $(A,b)$ is locally feasible if there exists an open neighborhood $U$ of $0$ such that for every $δ\in U$ there exists $x$ satisfying $A(δ)x\ge b(δ)$ entry-wise. For $d=1$ we construct a polynomial time algorithm for deciding local feasibility. For $d \ge 2$ we show local feasibility is NP-hard. This also gives the first polynomial-time algorithm for the asymptotic linear program problem introduced by Jeroslow in 1973. As an application (which was the primary motivation for this work) we give a computer-assisted proof of ergodicity of the following elementary 1D cellular automaton: given the current state $η_t \in \{0,1\}^{\mathbb{Z}}$ the next state $η_{t+1}(n)$ at each vertex $n\in \mathbb{Z}$ is obtained by $η_{t+1}(n)= \text{NAND}\big(\text{BSC}_δ(η_t(n-1)), \text{BSC}_δ(η_t(n))\big)$. Here the binary symmetric channel $\text{BSC}_δ$ takes a bit as input and flips it with probability $δ$ (and leaves it unchanged with probability $1-δ$). It is shown that there exists $δ_0>0$ such that for all $0<δ<δ_0$ the distribution of $η_t$ converges to a unique stationary measure irrespective of the initial condition $η_0$. We also consider the problem of broadcasting information on the 2D-grid of noisy binary-symmetric channels $\text{BSC}_δ$, where each node may apply an arbitrary processing function to its input bits. We prove that there exists $δ_0'>0$ such that for all noise levels $0<δ<δ_0'$ it is impossible to broadcast information for any processing function, as conjectured by Makur, Mossel and Polyanskiy.

cs.DS↗

arXiv2020

Generalizing Complex Hypotheses on Product Distributions: Auctions, Prophet Inequalities, and Pandora's Problem

This paper explores a theory of generalization for learning problems on product distributions, complementing the existing learning theories in the sense that it does not rely on any complexity measures of the hypothesis classes. The main contributions are two general sample complexity bounds: (1) $\tilde{O} \big( \frac{nk}{ε^2} \big)$ samples are sufficient and necessary for learning an $ε$-optimal hypothesis in any problem on an $n$-dimensional product distribution, whose marginals have finite supports of sizes at most $k$; (2) $\tilde{O} \big( \frac{n}{ε^2} \big)$ samples are sufficient and necessary for any problem on $n$-dimensional product distributions if it satisfies a notion of strong monotonicity from the algorithmic game theory literature. As applications of these theories, we match the optimal sample complexity for single-parameter revenue maximization (Guo et al., STOC 2019), improve the state-of-the-art for multi-parameter revenue maximization (Gonczarowski and Weinberg, FOCS 2018) and prophet inequality (Correa et al., EC 2019), and provide the first and tight sample complexity bound for Pandora's problem.

cs.GT↗

arXiv2019

Smoothed complexity of local Max-Cut and binary Max-CSP

We show that the smoothed complexity of the FLIP algorithm for local Max-Cut is at most $\smash{ϕn^{O(\sqrt{\log n})}}$, where $n$ is the number of nodes in the graph and $ϕ$ is a parameter that measures the magnitude of perturbations applied on its edge weights. This improves the previously best upper bound of $ϕn^{O(\log n)}$ by Etscheid and Röglin. Our result is based on an analysis of long sequences of flips, which shows~that~it is very unlikely for every flip in a long sequence to incur a positive but small improvement in the cut weight. We also extend the same upper bound on the smoothed complexity of FLIP to all binary Maximum Constraint Satisfaction Problems.

cs.DS↗

arXiv2019

Decomposition of symmetric multipartite observable

Production and verification of multipartite quantum state are an essential step in quantum information processing. In this work, we propose an efficient method to decompose symmetric multipartite observables, which are invariant under permutations between parties, with only $(N+1)(N+2)/2$ local measurement settings, where $N$ is the number of qubits. We apply the decomposition technique to evaluate the fidelity between an unknown prepared state and any target permutation invariant state. In addition, for some typical permutation invariant states, such as the Dicke state with a constant number of excitations, $m$, we derive a tight linear bound on the number of local measurement settings, $m(2m+3)N+1$. Meanwhile, for the $GHZ$ state, the $W$ state, and the Dicke state, we prove a linear lower bound, $Θ(N)$. Hence, for these particular states, our decomposition technique is optimal.

quant-ph↗

arXiv2019

Settling the Sample Complexity of Single-parameter Revenue Maximization

This paper settles the sample complexity of single-parameter revenue maximization by showing matching upper and lower bounds, up to a poly-logarithmic factor, for all families of value distributions that have been considered in the literature. The upper bounds are unified under a novel framework, which builds on the strong revenue monotonicity by Devanur, Huang, and Psomas (STOC 2016), and an information theoretic argument. This is fundamentally different from the previous approaches that rely on either constructing an $ε$-net of the mechanism space, explicitly or implicitly via statistical learning theory, or learning an approximately accurate version of the virtual values. To our knowledge, it is the first time information theoretical arguments are used to show sample complexity upper bounds, instead of lower bounds. Our lower bounds are also unified under a meta construction of hard instances.

cs.GT↗