arXiv subjects

Sichen Wang

Publications and source records attributed to Sichen Wang.

11 recordsLinked to original sources

arXiv2026

The Value of Steiner Hubs in Two-Hop Distance Labeling

Two-hop distance labelings were introduced in 2002 by Cohen, Halperin, Kaplan, and Zwick with hubs of two kinds: vertices of the graph, or, in their Steiner variant, arbitrary objects carrying arbitrary real values. On no family is the value of that freedom known. We determine it on $\ell_1$ products of betweenness-free metrics, those with no point between two others, a class containing every Hamming graph. The freedom is worth nothing when the factors have at most three letters, while from four letters on the largest saving is polynomial in the size of the product, attained on products of positively weighted stars. The $d$-dimensional hypercube is the two-letter case, and labeling it takes $(5/2+o(1))^d$ entries even with arbitrary hubs, matching the vertex-hub optimum of Goldberg, Razenshteyn, and Savchenko. Every lower bound here comes from one semidefinite program on a single factor, whose value $Λ$ never exceeds the rate that vertex hubs already achieve on the Hamming graph; where $Λ$ meets that ceiling, the freedom is worth nothing, and the ceiling is met exactly up to three letters.

cs.DS↗

arXiv2026

The Movement Complexity of Sorting

The complexity of sorting is usually measured by the number of comparisons. This measure ignores the movement of the read heads between comparisons, which is a real cost on many machines. We study this cost on its own. Keys lie on a $d$-dimensional grid, two heads move over the grid and compare the keys beneath them, and the only cost is the total movement of the heads. The algorithm plans its route in $r$ rounds and sees the outcomes of each round only after running it. For every $d$ and $r$ we determine the expected movement needed to sort $n$ keys: it is $n^β$ up to polylogarithmic factors, where $β=1+D^{r-1}/(D^{r}-(D-1)^{r})$ and $D=2d$, falling from $n^{2}$ at $r=1$ to $n^{1+1/(2d)}$ with unlimited rounds. Our algorithm makes every round move about the same amount, and a matching lower bound holds against every algorithm.

cs.DS↗

arXiv2026

WenSight-Decision-1 for Direct Decisions under E-commerce Rules

E-commerce decisions require applying natural-language rules to the available case evidence. We introduce WenSight-Decision-1, a shared model that scores supplied options directly from rules and case information for six operational tasks, with examples spanning six languages. We fine-tune Qwen3.5-9B with reference options as supervision, using the same option scores for training and inference. On 1,440 synthetic operational cases reserved for final evaluation, accuracy rises from 61.60% for Qwen3.5-9B to 92.92% for WenSight-Decision-1 under identical inputs and scoring. Joint fine-tuning improves all six tasks, bringing heterogeneous operational judgments under a common decision interface.

cs.CL↗

arXiv2026

A Tight Fractional Version of Generalized Tuza's Conjecture

For an $r$-uniform hypergraph $H$, let $ν(H)$ be the maximum number of edges no two of which share $r-1$ vertices, and $τ(H)$ the minimum number of $(r-1)$-sets such that every edge contains one of them. Aharoni and Zerbib conjectured that $τ(H)\le\lceil\frac{r+1}{2}\rceil\,ν(H)$, which for $r=3$ generalizes Tuza's conjecture on triangles. We prove that the fractional relaxation $τ^*(H)$ of $τ(H)$ satisfies $τ^*(H)\le\frac{r+1}{2}\,ν(H)$. This constant is best possible for every $r$, and for $r\ge4$ it improves on the previous bound of roughly $3r/4$.

math.CO↗

arXiv2026

On Completion Times under Memoryless Catastrophe

We study the completion time of a task subject to independent reset (catastrophe) at each step. The completion-time PGF depends on the base-process PGF through an affine relation, and we exploit this structure systematically. Our main result shows that, among age-based catastrophe mechanisms, geometric-tail catastrophe is exactly the class that yields uniform affine PGF structure; in continuous time, the characterization sharpens to Poisson resetting. We establish a sharp two-sided Kolmogorov bound of order $p+|α|$ for the exponential approximation $d_K(T/E[T], \mathrm{Exp}(1))$, thereby closing a logarithmic gap. Applications to the coupon collector with reset coupons reveal a discontinuous Gumbel-to-Exponential transition under resetting, while a multi-phase model exhibits a Gaussian-to-exponential transition with exponential convergence rate.

math.PR↗

arXiv2026

Retained-Set Descent for Diagonal Ramsey Numbers

We study how far a fixed Ramsey upper bound can be improved by descending through blue neighborhoods in one vertex set while keeping a second set fixed. A weighted inequality in the two set sizes determines when the descent can stop. For the source bound specified here, the infimum diagonal exponent over all finite derivations lies in $[1.305,\,1.307]$. A finite derivation gives $R(k,k)\le3.69507^k$ for all sufficiently large $k$; a concave polygon proves the lower bound for every finite depth. We also characterize the infimum as a greatest fixed point and show that every larger exponent has a finite derivation valid uniformly for nearby clique-size ratios.

math.CO↗

arXiv2026

A Bound Below 2.8 for Tuza's Conjecture

Let $ν(G)$ be the maximum number of edge-disjoint triangles in a graph $G$ and $τ(G)$ the minimum number of edges meeting every triangle. Tuza conjectured that $τ(G)\le 2ν(G)$. We prove that $τ(G)\le (165/59)ν(G)$. The constant $165/59\approx 2.797$ improves the bound $66/23\approx 2.870$ that Haxell proved in 1999. The key observation is that, for a suitable red-blue coloring, the families left over in Haxell's construction contain every triangle with exactly one red edge. Such a family $\mathcal{F}$ admits an exchange that forces certain red edges to lie in a single triangle once the blue edges of a maximum packing are deleted, which gives $τ(\mathcal{F})\le (8/3)ν(\mathcal{F})$.

math.CO↗

arXiv2026

The Minimax Rate of Denoising Flows on Trees

Isotonic regression and mean estimation over a simplex are among the most classical denoising problems under geometric constraints. Chatterjee and Lafferty generalized both to the recovery of a flow on a rooted tree from Gaussian noise, with isotonic regression on a path and the simplex on a star. Their results reach only special trees; on a general tree the minimax risk remained unknown for a decade. We settle the question in full. On every tree with $n$ vertices, at every budget $V$ and noise level $σ$, the minimax risk is of order $\min\{V^2H_T,\ σ^2k_0\}$, with $H_T$ the diameter and $k_0$ the crossing index of a truncated ancestor profile. A deterministic estimator, an exponentially weighted aggregate over integer states, attains it in $O(n^2\log(n+1))$ arithmetic operations. Least squares at a known budget, the natural convex program for the model, is suboptimal in the worst case by a factor of order $(\log n)^{2/5}$. One functional, the truncated ancestor profile, carries the rate, the estimator, and the least squares comparison. It serves as covering radius, as packing entropy in the positive cone, and as the range of the one-dimensional state behind the exact computation. Two classical theories become one on trees, sharp and computable throughout.

math.ST↗

arXiv2026

The Price of Order in the Logarithmic Method

The logarithmic method is a classical static-to-dynamic transformation: it stores one dynamic ordered set as several immutable static components and rebuilds them by merges. The same component-and-merge discipline underlies write-optimized ordered indexes, where cheap insertions must be reconciled with exact ordered queries. In this paper, we study the insertion-only version after $n$ insertions, over abstract keys, in a strongly materialized merge-stack model with sequential component merges and one forward scan of the live components per query. We bound the product between the total amount of data written during the $n$ insertions and the worst-case amount of data read by a single query, known as the write-read product. The optimal bounds are as follows: - Membership and local certificates: $Θ(n\log^2 n)$. - Order and range queries with named keys or endpoints: $Θ(n\log^3 n)$. - Select: $Θ(n^2)$. Thus, the logarithmic method does not impose a universal dynamic overhead: under materialized one-way access, the optimum depends on what information the query reveals before the scan starts. This pinpoints the access-model obstruction behind the extra logarithm for exact order and range queries, and the quadratic barrier for select.

cs.DS↗

arXiv2026

Depth over Fidelity in Fixed-Budget Noisy Evolution Strategies

Noisy evolution strategies under fixed evaluation budgets face a depth-fidelity trade-off: spending evaluations to denoise intra-generation rankings reduces the number of distribution updates the optimizer can execute. We argue for depth over fidelity and propose probabilistic elite membership (PEM), which replaces hard rank-based weights in evolution strategies with conditional expected rank weights that integrate over ranking uncertainty. PEM preserves the conditional mean update while reducing conditional update dispersion, a Rao-Blackwellization of the noisy rank-based step. We instantiate PEM via residual bootstrapping (RB-PEM) with capped per-generation overhead, complemented by an adaptive probe-and-switch mechanism for low-noise regimes. Across the COCO bbob-noisy suite and external tasks including RL policy search and hyperparameter optimization, RB-PEM achieves consistent gains in high-misranking, budget-constrained settings.

cs.NE↗

arXiv2022

Temporal and Contextual Transformer for Multi-Camera Editing of TV Shows

The ability to choose an appropriate camera view among multiple cameras plays a vital role in TV shows delivery. But it is hard to figure out the statistical pattern and apply intelligent processing due to the lack of high-quality training data. To solve this issue, we first collect a novel benchmark on this setting with four diverse scenarios including concerts, sports games, gala shows, and contests, where each scenario contains 6 synchronized tracks recorded by different cameras. It contains 88-hour raw videos that contribute to the 14-hour edited videos. Based on this benchmark, we further propose a new approach temporal and contextual transformer that utilizes clues from historical shots and other views to make shot transition decisions and predict which view to be used. Extensive experiments show that our method outperforms existing methods on the proposed multi-camera editing benchmark.

cs.CV↗