arXiv subjects

Yibin Zhao

Publications and source records attributed to Yibin Zhao.

9 recordsLinked to original sources

arXiv2026

Partially-Dynamic All-Pairs Maxflow and Effective Resistance via Stable Sparsifiers

We give a randomized data structure for undirected weighted graphs that are partially dynamic, i.e., that undergo either only edge insertions or only edge deletions. The data structure maintains $(1\pmε)$-approximations to the maxflow value and effective resistance between any queried pair of vertices, with total update time $\widetilde{O}_ε(n^2)$ and worst-case query time $\widetilde{O}_ε(1)$. Thus, for dense graphs where $m = Ω(n^2)$, our guarantees are near-optimal. Our algorithms succeed with high probability against an adaptive adversary. Our result follows from a simple stability principle for partially dynamic graphs. We show how to partition an online sequence of $m$ updates into $\widetilde{O}(n/ε)$ epochs such that every graph within an epoch is a $(1\pm O(ε))$-spectral approximation of the graph at the beginning of the epoch. The epochs are determined by the cumulative leverage score of the updated edges: small leverage-score mass implies small spectral change, while the total leverage-score mass over a monotone update sequence is $\widetilde{O}(n)$. Consequently, a spectral sparsifier needs to be recomputed only once per epoch. Applying known static all-pairs maxflow and effective-resistance oracles to these sparsifiers then yields the result.

cs.DS↗

arXiv2026

An Online Sparsification Algorithm from the Book

In their seminal paper [Cohen et al., 2016], Cohen, Musco, and Pachocki proposed a natural and simple online spectral sparsification algorithm: rows $a_1, a_2, \ldots \in \mathbb{R}^d$ of a matrix $A$ arrive one-by-one, and when row $a_i$ arrives, it is appended to sparsifier $\tilde{A}$ (after appropriately reweighting it) with probability proportional to its current leverage score $$ τ^{\mathrm{OL}}(a_i)=a_i^\top(A_i^\top A_i)^\dagger a_i, \text{ where }A_i = [a_1, a_2, \ldots, a_i]^\top $$ or otherwise discarded forever. For oblivious streams, they showed that this maintains a $(1\pmε)$-spectral approximation $\tilde{A}$ of every $A$ with $O(dε^{-2}\log^2 d)$ many rows. A natural question is whether the same algorithm works for adaptive streams, where each row may depend on the algorithm's previous random choices. The original proof does not extend directly: it analyzes the process in isotropic position with respect to the final matrix $A$, which is not fixed in advance under adaptivity. As an extension of this proof framework remained elusive, various algorithmic variants have since been suggested. In this paper, we show that the original online leverage-score sampling algorithm is indeed robust to adaptive adversaries. Our main technical contribution is a Freedman-type matrix martingale inequality with an evolving isotropic map, allowing the isotropic map used in the concentration argument to change with the stream. As a consequence, this gives the first online sparsification algorithm for adaptive streams that yields a sparsifier of near-optimal size $O(d \varepsilon^{-2}\log^2 d)$ whose working memory is proportional to the size of the sparsifier. For the special case of spectral graph sparsification, we provide an implementation that additionally runs in time near-linear in the stream size.

cs.DS↗

arXiv2026

$\text{VG}^2$GT: Voxel-Gaussian Splatting Visual Geometry Grounded Transformer

Gaussian splatting has shown strong potential for 3D reconstruction and novel view synthesis. However, most existing methods require accurate camera parameters and per-scene optimization, while feed-forward methods with pixel-aligned Gaussian primitives often suffer from artifacts and non-uniform primitives. In this paper, we propose $\text{VG}^2$GT, a Voxel-Gaussian Splatting Visual Geometry-Grounded Transformer. $\text{VG}^2$GT leverages a frozen pretrained visual foundation model (VFM), incorporates a multi-scale differentiable voxel module to enhance geometric understanding, and directly splits and regresses Gaussian primitive parameters from voxel features. During training, depth maps are supervised through stochastic solid volume rendering, enabling geometrically accurate Gaussian scene reconstruction while keeping the visual foundation model fully frozen. This design enables $\text{VG}^2$GT to be seamlessly plugged into any patch-feature-based VFM, while substantially reducing the required training cost. $\text{VG}^2$GT outperforms current state-of-the-art methods on widely used DTU, Replica, TAT, and ScanNet datasets.

cs.CV↗

arXiv2026

Semantic Triplet Restoration: A Novel Protocol for Hierarchical Table Understanding in Large Language Models

Table question answering requires models to recover semantic relations encoded implicitly by two-dimensional layout, merged cells, and hierarchical headers. Current pipelines typically use HTML or Markdown as intermediate table representations, but these layout-oriented serializations introduce markup overhead and require large language models to infer header-cell alignments from row and column spans. We propose Semantic Triplet Restoration (STR), a protocol that rewrites each cell as an atomic fact , where the item path specifies the row-wise entity, the feature path specifies the hierarchical attribute, and the value contains the cell content. We also present TripletQL, a lightweight query-aware router that uses STR to select an appropriate rendering or filtered subset of triplets for each question. Across four Chinese and English table-QA benchmarks, STR matches or improves upon HTML-based baselines while reducing input tokens. The relative benefit grows for smaller language models and longer table contexts, suggesting that explicit semantic representations are especially useful under constrained inference budgets. Code and data are available at https://github.com/Phoenix-ni/STR.git .

cs.CL↗

arXiv2026

FSFSplatter: Build Surface and Novel Views with Sparse-Views within 2min

Gaussian Splatting has become a leading reconstruction technique, known for its high-quality novel view synthesis and detailed reconstruction. However, most existing methods require dense, calibrated views. Reconstructing from free sparse images often leads to poor surface due to limited overlap and overfitting. We introduce FSFSplatter, a new approach for fast surface reconstruction from free sparse images. Our method integrates end-to-end dense Gaussian initialization, camera parameter estimation, and geometry-enhanced scene optimization. Specifically, FSFSplatter employs a large Transformer to encode multi-view images and generates a dense and geometrically consistent Gaussian scene initialization via a self-splitting Gaussian head. It eliminates local floaters through contribution-based pruning and mitigates overfitting to limited views by leveraging depth and multi-view feature supervision with differentiable camera parameters during rapid optimization. FSFSplatter outperforms current state-of-the-art methods on widely used DTU, Replica, and BlendedMVS datasets.

cs.CV↗

arXiv2025

Fully Dynamic Spectral and Cut Sparsifiers for Directed Graphs

Recent years have seen extensive research on directed graph sparsification. In this work, we initiate the study of fast fully dynamic spectral and cut sparsification algorithms for directed graphs. We introduce a new notion of spectral sparsification called degree-balance preserving spectral approximation, which maintains the difference between the in-degree and out-degree of each vertex. The approximation error is measured with respect to the corresponding undirected Laplacian. This notion is equivalent to direct Eulerian spectral approximation when the input graph is Eulerian. Our algorithm achieves an amortized update time of $O(\varepsilon^{-2} \cdot \text{polylog}(n))$ and produces a sparsifier of size $O(\varepsilon^{-2} n \cdot \text{polylog}(n))$. Additionally, we present an algorithm that maintains a constant-factor approximation sparsifier of size $O(n \cdot \text{polylog}(n))$ against an adaptive adversary for $O(\text{polylog}(n))$-partially symmetrized graphs, a notion introduced in [Kyng-Meierhans-Probst Gutenberg '22]. A $β$-partial symmetrization of a directed graph $\vec{G}$ is the union of $\vec{G}$ and $β\cdot G$, where $G$ is the corresponding undirected graph of $\vec{G}$. This algorithm also achieves a polylogarithmic amortized update time. Moreover, we develop a fully dynamic algorithm for maintaining a cut sparsifier for $β$-balanced directed graphs, where the ratio between weighted incoming and outgoing edges of any cut is at most $β$. This algorithm explicitly maintains a cut sparsifier of size $O(\varepsilon^{-2}βn \cdot \text{polylog}(n))$ in worst-case update time $O(\varepsilon^{-2}β\cdot \text{polylog}(n))$.

cs.DS↗

arXiv2024

Eulerian Graph Sparsification by Effective Resistance Decomposition

We provide an algorithm that, given an $n$-vertex $m$-edge Eulerian graph with polynomially bounded weights, computes an $\breve{O}(n\log^{2} n \cdot \varepsilon^{-2})$-edge $\varepsilon$-approximate Eulerian sparsifier with high probability in $\breve{O}(m\log^3 n)$ time (where $\breve{O}(\cdot)$ hides $\text{polyloglog}(n)$ factors). Due to a reduction from [Peng-Song, STOC '22], this yields an $\breve{O}(m\log^3 n + n\log^6 n)$-time algorithm for solving $n$-vertex $m$-edge Eulerian Laplacian systems with polynomially-bounded weights with high probability, improving upon the previous state-of-the-art runtime of $Ω(m\log^8 n + n\log^{23} n)$. We also give a polynomial-time algorithm that computes $O(\min(n\log n \cdot \varepsilon^{-2} + n\log^{5/3} n \cdot \varepsilon^{-4/3}, n\log^{3/2} n \cdot \varepsilon^{-2}))$-edge sparsifiers, improving the best such sparsity bound of $O(n\log^2 n \cdot \varepsilon^{-2} + n\log^{8/3} n \cdot \varepsilon^{-4/3})$ [Sachdeva-Thudi-Zhao, ICALP '24]. Finally, we show that our techniques extend to yield the first $O(m\cdot\text{polylog}(n))$ time algorithm for computing $O(n\varepsilon^{-1}\cdot\text{polylog}(n))$-edge graphical spectral sketches, as well as a natural Eulerian generalization we introduce. In contrast to prior Eulerian graph sparsification algorithms which used either short cycle or expander decompositions, our algorithms use a simple efficient effective resistance decomposition scheme we introduce. Our algorithms apply a natural sampling scheme and electrical routing (to achieve degree balance) to such decompositions. Our analysis leverages new asymmetric variance bounds specialized to Eulerian Laplacians and tools from discrepancy theory.

cs.DS↗

arXiv2023

Better Sparsifiers for Directed Eulerian Graphs

Spectral sparsification for directed Eulerian graphs is a key component in the design of fast algorithms for solving directed Laplacian linear systems. Directed Laplacian linear system solvers are crucial algorithmic primitives to fast computation of fundamental problems on random walks, such as computing stationary distribution, hitting and commute time, and personalized PageRank vectors. While spectral sparsification is well understood for undirected graphs and it is known that for every graph $G,$ $(1+\varepsilon)$-sparsifiers with $O(n\varepsilon^{-2})$ edges exist [Batson-Spielman-Srivastava, STOC '09] (which is optimal), the best known constructions of Eulerian sparsifiers require $Ω(n\varepsilon^{-2}\log^4 n)$ edges and are based on short-cycle decompositions [Chu et al., FOCS '18]. In this paper, we give improved constructions of Eulerian sparsifiers, specifically: 1. We show that for every directed Eulerian graph $\vec{G},$ there exist an Eulerian sparsifier with $O(n\varepsilon^{-2} \log^2 n \log^2\log n + n\varepsilon^{-4/3}\log^{8/3} n)$ edges. This result is based on combining short-cycle decompositions [Chu-Gao-Peng-Sachdeva-Sawlani-Wang, FOCS '18, SICOMP] and [Parter-Yogev, ICALP '19], with recent progress on the matrix Spencer conjecture [Bansal-Meka-Jiang, STOC '23]. 2. We give an improved analysis of the constructions based on short-cycle decompositions, giving an $m^{1+δ}$-time algorithm for any constant $δ> 0$ for constructing Eulerian sparsifiers with $O(n\varepsilon^{-2}\log^3 n)$ edges.

cs.DS↗

arXiv2023

A Simple and Efficient Parallel Laplacian Solver

A symmetric matrix is called a Laplacian if it has nonpositive off-diagonal entries and zero row sums. Since the seminal work of Spielman and Teng (2004) on solving Laplacian linear systems in nearly linear time, several algorithms have been designed for the task. Yet, the work of Kyng and Sachdeva (2016) remains the simplest and most practical sequential solver. They presented a solver purely based on random sampling and without graph-theoretic constructions such as low-stretch trees and sparsifiers. In this work, we extend the result of Kyng and Sachdeva to a simple parallel Laplacian solver with $O(m \log^3 n \log\log n)$ or $O((m + n\log^5 n)\log n \log\log n)$ work and $O(\log^2 n \log\log n)$ depth using the ideas of block Cholesky factorization from Kyng et al. (2016). Compared to the best known parallel Laplacian solvers that achieve polylogarithmic depth due to Lee et al. (2015), our solver achieves both better depth and, for dense graphs, better work.

cs.DS↗