数据结构与算法

We study the problem of approximating the diameter of directed graphs under the min-distance measure, defined as $d_{\min}(u,v) = \min(d(u,v), d(v,u))$. Unlike standard shortest-path distance, min-distance is not a metric, which renders…

Terminal embeddings have emerged as a powerful tool for dimension reduction. Given a set of points $P\subset \mathbb{R}^d$, a terminal embedding is a mapping $f:\mathbb{R}^d\rightarrow \mathbb{R}^t$ that preserves the pairwise distance…

We introduce a streaming model that uses both catalytic and regular memory. In this model, we show how to exactly compute the frequency moments using a logarithmic number of bits of regular memory and a polynomial number of bits of…

We introduce a new notion of distance between two graph states $|G\rangle$ and $|G'\rangle$ on the same set of qubits. This distance is the minimum number of ancilla qubits in a graph state $|\widehat{G}\rangle$ from which both $|G\rangle$…

In this work, we initiate the study of strongly refuting the satisfiability of random ordering constraint satisfaction problems. We show that there is a polynomial-time $\varepsilon$-refutation algorithm for random ordering CSP with…

The Irrelevant Vertex Technique is one of the cornerstones of algorithmic graph theory, underlying Robertson and Seymour's algorithm for \textsc{Disjoint Paths} and much of the algorithmic Graph Minors theory. We show that, in the setting…

We study the problem of computing an envy-free (EF) allocation of $m$ indivisible items among $n$ agents when items come in three distinct types. Each agent holds additive valuations over item types that may be positive (goods), negative…

We present a polynomial-time algorithm for optimally coloring perfect graphs that is based entirely on graph-theoretic operations. At its core, the algorithm decides whether a perfect graph contains a clique of a given size by iteratively…

We study exact algorithms for Equal-Subset-Sum in the worst-case setting: given a set $S$ of $n$ integers, find two distinct subsets $A,B\subseteq S$ whose sums are equal. We establish a new state-of-the-art bound for this problem by…

Contention resolution schemes (CRS) are a fundamental and widely applied tool for rounding fractional solutions subject to combinatorial constraints. However, the known analyses of CRS generally only guarantee lower bounds on the expected…

We study non-clairvoyant scheduling for batched Large Language Model (LLM) inference under a hard Key-Value (KV) cache memory budget. Each request has a known prompt length but an unknown response length, and its memory footprint comprises…

We extend G{\aa}rding's theorem to homogeneous posynomials: if a finite positive sum of monomials with arbitrary nonnegative real exponents is zero-free on a product of right half-planes, then its degree-normalized root is concave.…

This paper studies graph matching under the correlated $\text{Erd\H{o}s-R\'{e}nyi}$ (ER) graph pair model. This model first samples an $\mathrm{ER}(n,\frac{\lambda}{ns})$ base graph, whose edges are then independently subsampled twice with…

We show that every weighted hypergraph on $n$ vertices admits a spectral $\varepsilon$-sparsifier with $O(n\log n/\varepsilon^2)$ hyperedges, strengthening the independent STOC 2023 works of Lee and Jambulapati--Liu--Sidford by removing…

In this paper we develop the framework of using a parametrized mapping $[\sigma(1), \sigma(2), \cdots, \sigma(n)] \mapsto \sigma(1)z + \sigma(2)z^2 + \cdots \sigma(n)z^n$ to perform runtime analysis on Shellsort. In particular, we show that…

Continual counting under pure differential privacy is one of the simplest and most well-studied problems in the continual observation model. Nevertheless, an asymptotic gap remains between the best known upper and lower bounds for maximum…

A \emph{generalized degenerate string} (GD) is a sequence $T=T_1\dots T_n$ of nonempty finite sets of strings, called \emph{segments}, such that all strings in a segment have the same length. Given a solid pattern $P$, GD string matching…

We introduce a streaming model with \emph{catalytic memory}, an auxiliary workspace that must be returned to its initial state at the end of the computation. We show that catalytic space yields dramatic space savings for data stream…

We provide a local computation algorithm to approximate the top eigenvector $x \in \mathbb{R}^n$ of a symmetric matrix $A \in \mathbb{R}^{n \times n}$ with entries between $-1$ and $1$, building on the work of Swartworth and Woodruff [SODA…

The Parking Permit Problem (PPP), first studied by Meyerson, is a classic online problem generalizing the ski rental problem. We re-examine the PPP using the primal-dual scheme, obtaining simple algorithms with superior performance…