Research
Research
Research
Research
483+ open-access research outputs.
We propose a new convex programming relaxation for the weighted Nash social welfare (NSW) problem that achieves a matching $(e^{1/e}\approx 1.445)$-approximation via the rounding algorithm of Feng and…
Perturbing a deterministic $n$-dimensional matrix with small Gaussian noise is a cornerstone of smoothed analysis of algorithms [Spielman and Teng, JACM 2004], as it reduces the condition number of th…
We present a search for small Kochen-Specker (KS) sets in dimension 3, specifically targeting extensions of the 13-ray Yu-Oh set, which has been proven to be the minimal witness to state-independent c…
We prove two results on the mixing times of Markov chains for two-spin systems. First, we show that the Glauber dynamics mixes in polynomial time for the Gibbs distributions of antiferromagnetic two-s…
We study the computational complexity of approximately computing the partition function of a spin system. Techniques based on standard counting-to-sampling reductions yield $\tilde{O}(n^2)$-time algor…
The fused multiply-add (FMA) instruction enables the radix-2 FFT butterfly to be computed in 6~FMA operations -- the proven minimum. The classical factorization by Linzer and Feig~\cite{linzer1993} pr…
Uniform interpolation is the property that, for any formula and set of atoms, there exists the strongest consequence omitting those atoms. It plays a central role in knowledge representation and reaso…
We resolve the long-standing open problem of Boolean dynamic data structure hardness, proving an unconditional lower bound of $\Omega((\log n / \log\log n)^2)$ for the Multiphase Problem of Patrascu […
In the GEODETIC SET problem, an input is a (di)graph $G$ and integer $k$, and the objective is to decide whether there exists a vertex subset $S$ of size $k$ such that any vertex in $V(G)\setminus S$ …
Consider $n$ points generated uniformly at random in the unit square, and let $L_n$ be the length of their optimal traveling salesman tour. Beardwood, Halton, and Hammersley (1959) showed $L_n / \sqrt…
A Random Access query to a string $T\in [0..\sigma)^n$ asks for the character $T[i]$ at a given position $i\in [0..n)$. In $O(n\log\sigma)$ bits of space, this fundamental task admits constant-time qu…
The 6G communication systems use mmWave and MIMO technologies to achieve wide bandwidth and high throughout, leading to indispensable need for beam alignment to overcome severe signal attenuation. Tra…
In downlink massive random access (DMRA), a base station transmits messages to a typically small subset of active users, selected randomly from a massive number of total users. Explicitly encoding the…
We study the optimal design of additive mechanisms for vector-valued queries under $\epsilon$-differential privacy (DP). Given only the sensitivity of a query and a norm-monotone cost function measuri…
We show that for $q$-colorings in $k$-uniform hypergraphs with maximum degree $\Delta$, if $k\ge 50$ and $q\ge 700\Delta^{\frac{5}{k-10}}$, there is a "Lee-Yang" zero-free strip around the interval $[…
Given a vertex in a $(k, \varphi, \epsilon)$-clusterable graph, i.e. a graph whose vertex set can be partitioned into a disjoint union of $\varphi$-expanders of size $\approx n/k$ with outer conductan…
The Model Context Protocol (MCP) (MCP Community, 2025) has emerged as a widely used framework for enabling LLM-based agents to communicate with external tools and services. The original MCP implementa…
We present a simple randomized algorithm that can efficiently maintain a $(\Delta+1)$ coloring as the graph undergoes edge insertion and deletion updates, where $\Delta$ denotes an upper bound on the …
Given a sequence $s_1$ of $n$ letters drawn i.i.d. from an alphabet of size $\sigma$ and a mutated substring $s_2$ of length $m < n$, we often want to recover the mutation history that generated $s_2$…
Suppose we are given an infinite sequence of input cells, each initialized with a uniform random symbol from $[n]$. How hard is it to output a sequence in $[n]^n$ that is close to a uniform random per…
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