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Wenzheng Li

Publications and source records attributed to Wenzheng Li.

12 recordsLinked to original sources
arXiv2026

Distributed Edge Coloring with Small Palettes and a Special Case of the Constructive Lovász Local Lemma

We explore the complexity of edge coloring in the LOCAL model in different palette size regimes. 1. Lower Bounds: First, we simplify the round elimination technique of Brandt et al. and prove that $(2Δ-2)$-edge coloring requires $Ω(\log_Δ\log n)$ time w.h.p. and $Ω(\log_Δn)$ time deterministically, even on trees. Second, we show that a natural approach to computing $(Δ+1)$-edge colorings (Vizing's theorem) via extending partial colorings by iteratively re-coloring parts of the graph in the worst case requires recoloring subgraphs of diameter $Ω(Δ\log n)$. 2. Upper Bounds on General Graphs: We give a randomized edge coloring algorithm that can use palette sizes as small as $Δ+ \tilde{O}(\sqrtΔ)$, which is a natural barrier for randomized approaches. Our algorithm employs a permissive version of the constructive Lovasz local lemma as a black box. The runtime of algorithm varies for different choices of $Δ$ and palette size. For example, our algorithm computes a $(1+ε)Δ$-edge coloring in $O(\log n)$ time when $ε\geq (\log^3 Δ) / \sqrtΔ$, or $O(\log_Δ n) + (\log \log n)^{3 + o(1)}$ time when $ε= Ω(1)$. 3. Upper Bounds on Trees: We show that the $Ω(\log_Δ\log n)$ lower bound can be nearly matched on trees. To establish this result, we develop a new distributed Lovasz local lemma algorithm for tree-structured dependency graphs. Specifically, our $(1+ε)Δ$-edge coloring algorithm for trees takes $O(\log(1 / ε)) \cdot \max\{\frac{\log\log n}{\log\log\log n},\, \log_{\log Δ} \log n\}$ time when $ε\geq (\log^3 Δ) / \sqrtΔ$, or $O\left( \max\{\frac{\log\log n}{\log\log\log n},\, \log_Δ \log n\}\right)$ time when $ε= Ω(1)$.

cs.DC↗
arXiv2026

Approximating Nash Social Welfare by Matching and Local Search

For any $\varepsilon>0$, we give a simple, deterministic $(4+\varepsilon)$-approximation algorithm for the Nash social welfare (NSW) problem under submodular valuations. We also consider the asymmetric variant of the problem, where the objective is to maximize the weighted geometric mean of agents' valuations, and give an $e (ω+ 2 + \varepsilon)$-approximation if the ratio between the largest weight and the average weight is at most $ω$. We also show that the $1/2$-EFX envy-freeness property can be attained simultaneously with a constant-factor approximation. More precisely, we can find an allocation in polynomial time that is both $1/2$-EFX and a $(8+\varepsilon)$-approximation to the symmetric NSW problem under submodular valuations.

cs.GT↗
arXiv2025

Multi-Head Spectral-Adaptive Graph Anomaly Detection

Graph anomaly detection technology has broad applications in financial fraud and risk control. However, existing graph anomaly detection methods often face significant challenges when dealing with complex and variable abnormal patterns, as anomalous nodes are often disguised and mixed with normal nodes, leading to the coexistence of homophily and heterophily in the graph domain. Recent spectral graph neural networks have made notable progress in addressing this issue; however, current techniques typically employ fixed, globally shared filters. This 'one-size-fits-all' approach can easily cause over-smoothing, erasing critical high-frequency signals needed for fraud detection, and lacks adaptive capabilities for different graph instances. To solve this problem, we propose a Multi-Head Spectral-Adaptive Graph Neural Network (MHSA-GNN). The core innovation is the design of a lightweight hypernetwork that, conditioned on a 'spectral fingerprint' containing structural statistics and Rayleigh quotient features, dynamically generates Chebyshev filter parameters tailored to each instance. This enables a customized filtering strategy for each node and its local subgraph. Additionally, to prevent mode collapse in the multi-head mechanism, we introduce a novel dual regularization strategy that combines teacher-student contrastive learning (TSC) to ensure representation accuracy and Barlow Twins diversity loss (BTD) to enforce orthogonality among heads. Extensive experiments on four real-world datasets demonstrate that our method effectively preserves high-frequency abnormal signals and significantly outperforms existing state-of-the-art methods, especially showing excellent robustness on highly heterogeneous datasets.

cs.LG↗
arXiv2023

A constant factor approximation for Nash social welfare with subadditive valuations

We present a constant-factor approximation algorithm for the Nash social welfare maximization problem with subadditive valuations accessible via demand queries. More generally, we propose a template for NSW optimization by solving a configuration-type LP and using a rounding procedure for (utilitarian) social welfare as a blackbox, which could be applicable to other variants of the problem.

cs.GT↗
arXiv2023

Dynamic brain spectrum acquired by a real-time ultra-spectral imaging chip with reconfigurable metasurfaces

Spectral imaging paves way for various fields and particular in biomedical research. However, spectral imaging mainly depending on spatial or temporal scanning, cannot achieve high temporal, spatial and spectral resolution simultaneously. In this study, we demonstrated a silicon real-time ultra-spectral imaging chip based on reconfigurable metasurfaces, comprising of 155,216 (356$\times$436) image-adaptive micro-spectrometers with ultra-high center-wavelength accuracy of 0.04 nm and spectral resolution of 0.8 nm. It is employed for imaging brain hemodynamics, and the dynamic spectral absorption properties of deoxyhemoglobin and oxyhemoglobin in a rat barrel cortex were obtained, which enlighten the spectroscopy in vivo studies and other real-time applications.

physics.optics↗
arXiv2021

Estimating the Nash Social Welfare for coverage and other submodular valuations

We study the Nash Social Welfare problem: Given $n$ agents with valuation functions $v_i:2^{[m]} \rightarrow {\mathbb R}$, partition $[m]$ into $S_1,\ldots,S_n$ so as to maximize $(\prod_{i=1}^{n} v_i(S_i))^{1/n}$. The problem has been shown to admit a constant-factor approximation for additive, budget-additive, and piecewise linear concave separable valuations; the case of submodular valuations is open. We provide a $\frac{1}{e} (1-\frac{1}{e})^2$-approximation of the {\em optimal value} for several classes of submodular valuations: coverage, sums of matroid rank functions, and certain matching-based valuations.

cs.GT↗
arXiv2020

A polynomial lower bound on adaptive complexity of submodular maximization

In large-data applications, it is desirable to design algorithms with a high degree of parallelization. In the context of submodular optimization, adaptive complexity has become a widely-used measure of an algorithm's "sequentiality". Algorithms in the adaptive model proceed in rounds, and can issue polynomially many queries to a function $f$ in each round. The queries in each round must be independent, produced by a computation that depends only on query results obtained in previous rounds. In this work, we examine two fundamental variants of submodular maximization in the adaptive complexity model: cardinality-constrained monotone maximization, and unconstrained non-mono-tone maximization. Our main result is that an $r$-round algorithm for cardinality-constrained monotone maximization cannot achieve an approximation factor better than $1 - 1/e - Ω(\min \{ \frac{1}{r}, \frac{\log^2 n}{r^3} \})$, for any $r < n^c$ (where $c>0$ is some constant). This is the first result showing that the number of rounds must blow up polynomially large as we approach the optimal factor of $1-1/e$. For the unconstrained non-monotone maximization problem, we show a positive result: For every instance, and every $δ>0$, either we obtain a $(1/2-δ)$-approximation in $1$ round, or a $(1/2+Ω(δ^2))$-approximation in $O(1/δ^2)$ rounds. In particular (and in contrast to the cardinality-constrained case), there cannot be an instance where (i) it is impossible to achieve an approximation factor better than $1/2$ regardless of the number of rounds, and (ii) it takes $r$ rounds to achieve a factor of $1/2-O(1/r)$.

cs.DS↗
arXiv2019

An Optimal Distributed $(Δ+1)$-Coloring Algorithm?

Vertex coloring is one of the classic symmetry breaking problems studied in distributed computing. In this paper we present a new algorithm for $(Δ+1)$-list coloring in the randomized ${\sf LOCAL}$ model running in $O(\mathsf{Det}_{\scriptscriptstyle d}(\text{poly} \log n))$ time, where $\mathsf{Det}_{\scriptscriptstyle d}(n')$ is the deterministic complexity of $(\text{deg}+1)$-list coloring on $n'$-vertex graphs. (In this problem, each $v$ has a palette of size $\text{deg}(v)+1$.) This improves upon a previous randomized algorithm of Harris, Schneider, and Su [STOC'16, JACM'18] with complexity $O(\sqrt{\log Δ} + \log\log n + \mathsf{Det}_{\scriptscriptstyle d}(\text{poly} \log n))$, and, for some range of $Δ$, is much faster than the best known deterministic algorithm of Fraigniaud, Heinrich, and Kosowski [FOCS'16] and Barenboim, Elkin, and Goldenberg [PODC'18], with complexity $O(\sqrt{Δ\log Δ}\log^\ast Δ+ \log^* n)$. Our algorithm "appears to be" optimal, in view of the $Ω(\mathsf{Det}(\text{poly} \log n))$ randomized lower bound due to Chang, Kopelowitz, and Pettie [FOCS'16], where $\mathsf{Det}$ is the deterministic complexity of $(Δ+1)$-list coloring. At present, the best upper bounds on $\mathsf{Det}_{\scriptscriptstyle d}(n')$ and $\mathsf{Det}(n')$ are both $2^{O(\sqrt{\log n'})}$ and use a black box application of network decompositions (Panconesi and Srinivasan [Journal of Algorithms'96]). It is quite possible that the true complexities of both problems are the same, asymptotically, which would imply the randomized optimality of our $(Δ+1)$-list coloring algorithm.

cs.DC↗
arXiv2017

Wasserstein Identity Testing

Uniformity testing and the more general identity testing are well studied problems in distributional property testing. Most previous work focuses on testing under $L_1$-distance. However, when the support is very large or even continuous, testing under $L_1$-distance may require a huge (even infinite) number of samples. Motivated by such issues, we consider the identity testing in Wasserstein distance (a.k.a. transportation distance and earthmover distance) on a metric space (discrete or continuous). In this paper, we propose the Wasserstein identity testing problem (Identity Testing in Wasserstein distance). We obtain nearly optimal worst-case sample complexity for the problem. Moreover, for a large class of probability distributions satisfying the so-called "Doubling Condition", we provide nearly instance-optimal sample complexity.

cs.LG↗
arXiv2017

The Energy Complexity of Broadcast

Energy is often the most constrained resource in networks of battery-powered devices, and as devices become smaller, they spend a larger fraction of their energy on communication (transceiver usage) not computation. As an imperfect proxy for true energy usage, we define energy complexity to be the number of time slots a device transmits/listens; idle time and computation are free. In this paper we investigate the energy complexity of fundamental communication primitives such as broadcast in multi-hop radio networks. We consider models with collision detection (CD) and without (No-CD), as well as both randomized and deterministic algorithms. Some take-away messages from this work include: 1. The energy complexity of broadcast in a multi-hop network is intimately connected to the time complexity of leader election in a single-hop (clique) network. Many existing lower bounds on time complexity immediately transfer to energy complexity. For example, in the CD and No-CD models, we need $Ω(\log n)$ and $Ω(\log^2 n)$ energy, respectively. 2. The energy lower bounds above can almost be achieved, given sufficient ($Ω(n)$) time. In the CD and No-CD models we can solve broadcast using $O(\frac{\log n\log\log n}{\log\log\log n})$ energy and $O(\log^3 n)$ energy, respectively. 3. The complexity measures of Energy and Time are in conflict, and it is an open problem whether both can be minimized simultaneously. We give a tradeoff showing it is possible to be nearly optimal in both measures simultaneously. For any constant $ε>0$, broadcast can be solved in $O(D^{1+ε}\log^{O(1/ε)} n)$ time with $O(\log^{O(1/ε)} n)$ energy, where $D$ is the diameter of the network.

cs.DC↗
arXiv2017

Adapting Low-Cost Platforms for Robotics Research

Validation of robotics theory on real-world hardware platforms is important to prove the practical feasibility of algorithms. This paper discusses some of the lessons learned while adapting the EvoBot, a low-cost robotics platform that we designed and prototyped, for research in diverse areas in robotics. The EvoBot platform was designed to be a low cost, open source, general purpose robotics platform intended to enable testing and validation of algorithms from a wide variety of sub-fields of robotics. Throughout the paper, we outline and discuss some common failures, practical limitations and inconsistencies between theory and practice that one may encounter while adapting such low-cost platforms for robotics research. We demonstrate these aspects through four representative common robotics tasks- localization, real-time control, swarm consensus and path planning applications, performed using the EvoBots. We also propose some potential solutions to the encountered problems and try to generalize them.

cs.RO↗