数据结构与算法

We study the computational complexity of finding the geodetic number of a graph on chordal graphs and interval graphs. A set $S$ of vertices of a graph $G$ is a \textit{geodetic set} if every vertex of $G$ lies in a shortest path between…

We initiate the study of property testing for $k$-submodular functions, a higher-dimensional analogue of submodular functions defined on partial partitions of a ground set. While $k$-submodularity retains the diminishing-returns flavor of…

The geometric median problem asks to find a point in $\mathbb{R}^d$ that minimizes the sum of Euclidean distances to an input set. It is a classical problem in computational geometry and appears as a subroutine in numerous optimization…

Cycle rank is a depth parameter for digraphs introduced by Eggan in 1963. Gruber (DMTCS 2012) and Giannopoulou, Hunter, and Thilikos (DAM 2012) asked whether the problem of determining if a given digraph has cycle rank at most $w$ is…

We provide algorithms that compute $\epsilon$-estimates of the $\ell_p$-Lewis weights of a matrix $A \in \mathbb{R}^{m \times n}$ for $p \geq 4$ using $O(p^2 \log(m/\epsilon))$ rounds of leverage score computation, where $\ell_p$-Lewis…

We study the problem of gossiping (all-to-all information exchange) in ad-hoc radio networks. Such a network is represented by a strongly-connected directed graph with \(n\) vertices, whose topology is initially unknown to the protocol. In…

We consider submodular maximization under increasing cardinality constraint and ask for a good incremental solution, i.e., an ordering of the ground set such that each prefix of the ordering yields a good solution for its respective…

We demonstrate that the problem of finding the maximum cut of a planar graph with arbitrary weights can be easily mapped to a minimum T-join problem in the absolute dual graph - the dual graph with absolute weights, as opposed to the known…

We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace. Lee, Mehrotra and Zampetakis (FOCS'24) recently obtained the first polynomial time algorithm for this problem, but their resulting…

In network vulnerability analysis, it is crucial to evaluate the robustness of $k$-cores against vertex removals. A $k$-core is often fragile since removing a few vertices can trigger a large reduction in the core size, a phenomenon known…

Given a graph, computing distances and reachabilities from a small set of vertices to the whole graph is an important primitive both in theory and in practice. In undirected unweighted graphs, while computing single-source shortest path…

In DIRECTED GEODETIC SET, we are given a (directed) graph and seek a small solution set $S \subseteq V(G)$ such that every vertex lies on a shortest directed path between two vertices in $S$. It is known that the problem is W[2]-hard when…

We study language generation in the limit under bounded memory. In this task, a learner observes examples from an unknown target language one at a time and must eventually output only new valid examples. Prior work assumes access to the…

Connected Submodular Maximization (CSM) is a graph problem with important applications to wireless network deployment, path planning, epidemic outbreaks, and cancer genome studies. In CSM, we are given a graph $G$, a non-negative monotone…

We give a randomized algorithm that samples a nearly uniform Eulerian tour of a directed Eulerian multigraph with $m$ arcs in $\widetilde O(m^{3/2})$ time. The guarantee is worst-case, applies to arbitrary directed Eulerian multigraphs, and…

Determining a linear utility function that correlates with observed candidate rankings is a foundational problem with applications in domains such as admissions, hiring, and recommendation systems, e.g., [Storandt and Funke, AAAI'19, Zhang…

We revisit the problem of Gaussian mean testing in a distributed, communication constrained setting, where each of $n$ users independently observes samples from an unknown $d$-dimensional spherical Gaussian distribution…

Clustering is a basic task in data analysis and machine learning, and the optimization of clustering objectives are well-studied optimization problems; amongst these, the $k$-Means objective is arguably the most well known. Given a…

We study exact predecessor and rank search in a routed, atom-budgeted, certified-repair learned-index architecture. An ordered directory routes each query to a contiguous interval, a counted local predictor returns a certified rank window,…

The $2 \rightarrow q$ norm of a matrix $X \in \mathbb{R}^{n \times d}$ is defined as $\lVert X \rVert_{2 \rightarrow q} = \sup_{\lVert v \rVert_2 = 1} \lVert Xv \rVert_q$. We give polynomial-time multiplicative approximation algorithms for…