数据结构与算法

In the Graph Scheduling problem we schedule a given multiset of edges on discrete time steps, such that at each step the set of edges forms a matching. The goal is to minimize the sum of weighted group completion times, where a group is a…

We give a constant-factor approximation algorithm for Max Dist-2 Independent Set in graphs of bounded radius-2 merge-width. The same result holds for Min Dominating Set from [Bonamy and Geniet, 2025], [Chan et al., SODA '12]. Both…

A quasi-metric $(T,\delta_T)$ is an Okamura-Seymour quasimetric if there exists an edge-weighted planar embedded directed graph $G = (V,E,w)$ such that $T$ is a set of terminals on the outerface of $G$ and $\delta_G(t,t') = \delta_T(t,t')$…

Suffixient arrays are recent structures that have attracted attention because they offer relevant pattern matching functionality in less asymptotic space than the Run-Length BWT, the de-facto standard to index highly repetitive string…

Contextual pattern matching is the task of, given a pattern $P[1,m]$, a context length $\lambda$, and a text $T[1,n]$, find all the $occ$ distinct contexts in which $P$ occurs in $T$, the context being the $\lambda$ symbols preceding and…

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…