数据结构与算法

Windowed recurrences are sliding window calculations where a function is applied iteratively across the window of data, and are ubiquitous throughout the natural, social, and computational sciences. In this monograph we explore the…

We propose a new approach to utilize quantum computers for binary linear programming (BLP), which can be extended to general integer linear programs (ILP). Quantum optimization algorithms, hybrid or quantum-only, are currently general…

The problem \textsc{Token Jumping} asks whether, given a graph $G$ and two independent sets of \emph{tokens} $I$ and $J$ of $G$, we can transform $I$ into $J$ by changing the position of a single token in each step and having an independent…

Given an undirected graph $G=(V, E)$, the Personalized PageRank (PPR) of $t\in V$ with respect to $s\in V$, denoted $\pi(s,t)$, is the probability that an $\alpha$-discounted random walk starting at $s$ terminates at $t$. We study the time…

This work addresses the well-known Maximum Independent Set problem in the context of hypergraphs. While this problem has been extensively studied on graphs, we focus on its strong extension to hypergraphs, where edges may connect any number…

In this paper, we continue the study of robust satisfiability of promise CSPs (PCSPs), initiated in (Brakensiek, Guruswami, Sandeep, STOC 2023 / Discrete Analysis 2025), and obtain the following results: For the PCSP 1-in-3-SAT vs NAE-SAT…

The online bisection problem requires maintaining a dynamic partition of $n$ nodes into two equal-sized clusters. Requests arrive sequentially as node pairs. If the nodes lie in different clusters, the algorithm pays unit cost. After each…

We investigate the parameterized complexity of Bayesian Network Structure Learning (BNSL), a classical problem that has received significant attention in empirical but also purely theoretical studies. We follow up on previous works that…

In the spanning-tree congestion problem ($\mathsf{STC}$), we are given a graph $G$, and the objective is to compute a spanning tree of $G$ that minimizes the maximum edge congestion. While $\mathsf{STC}$ is known to be $\mathbb{NP}$-hard,…

This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…

In length-constrained minimum spanning tree (MST) we are given an $n$-node graph $G = (V,E)$ with edge weights $w : E \to \mathbb{Z}_{\geq 0}$ and edge lengths $l: E \to \mathbb{Z}_{\geq 0}$ along with a root node $r \in V$ and a…

We study the \textsc{Labeled Contractibility} problem, where the input consists of two vertex-labeled graphs $G$ and $H$, and the goal is to determine whether $H$ can be obtained from $G$ via a sequence of edge contractions. Lafond and…

The problem of CSP sparsification asks: for a given CSP instance, what is the sparsest possible reweighting such that for every possible assignment to the instance, the number of satisfied constraints is preserved up to a factor of $1 \pm…

An evaluator, such as an LLM-as-a-judge, is trustworthy when there exists some agreed-upon way to measure its performance as a labeller. Traditional approaches either rely on testing the evaluator against references or assume that it…

We propose new abstract and unified perspectives on a range of scheduling and graph coloring problems with general min-sum objectives. Specifically, we consider various problems where the objective function is the weighted sum of completion…

As one of the most fundamental problems in graph processing, the Single-Source Shortest Path (SSSP) problem plays a critical role in numerous application scenarios. However, existing GPU-based solutions remain inefficient, as they typically…

Given a set of strings over a specified alphabet, identifying a median or consensus string that minimizes the total distance to all input strings is a fundamental data aggregation problem. When the Hamming distance is considered as the…

We study approximation algorithms for Maximum Constraint Satisfaction Problems (Max-CSPs) under differential privacy (DP) where the constraints are considered sensitive data. Information-theoretically, we aim to classify the best…

This paper presents a new deterministic algorithm for single-source shortest paths (SSSP) on real non-negative edge-weighted directed graphs, with running time $O(m\sqrt{\log n}+\sqrt{mn\log n\log \log n})$, which is $O(m\sqrt{\log n\log…

Evaluating a polynomial on a set of points is a fundamental task in computer algebra. In this work, we revisit a particular variant called trimmed multipoint evaluation: given an $n$-variate polynomial with bounded individual degree $d$ and…