数据结构与算法

We study a Bayesian binary sequential hypothesis testing problem with multiple large language models (LLMs). Each LLM $j$ has per-query cost $c_j>0$, random waiting time with mean $\mu_j>0$ and sub-Gaussian tails, and \emph{asymmetric}…

We obtain better algorithms for computing more balanced orientations and degree splits in LOCAL. Important to our result is a connection to the hypergraph sinkless orientation problem [BMNSU, SODA'25] We design an algorithm of complexity…

For any $\Delta$, let $k_\Delta$ be the maximum integer $k$ such that $(k+1)(k+2)\le \Delta$. We give a distributed \LOCAL algorithm that, given an integer $k < k_\Delta$, computes a valid $\Delta-k$-coloring if one exists. The algorithm…

We initiate an investigation of node differential privacy for graphs in the local model of private data analysis. In our model, dubbed LNDP*, each node sees its own edge list and releases the output of a local randomizer on this input.…

We consider the Euclidean $k$-means clustering problem in a dynamic setting, where we have to explicitly maintain a solution (a set of $k$ centers) $S \subseteq \mathbb{R}^d$ subject to point insertions/deletions in $\mathbb{R}^d$. We…

Given a graph $G=(V,E)$, a $\beta$-ruling set is a subset $S\subseteq V$ that is i) independent, and ii) every node $v\in V$ has a node of $S$ within distance $\beta$. In this paper we present almost optimal distributed algorithms for…

Branch-and-bound algorithms (B&B) and polynomial-time approximation schemes (PTAS) are two seemingly distant areas of combinatorial optimization. We intend to (partially) bridge the gap between them while expanding the boundary of…

In well-studied graph modification problems, adding and deleting vertices and edges are used as graph editing operations. We propose a model for graph modification on geometric intersection graphs called Geometric Graph Edit Distance that…

We prove that any algorithm computing the sum-exclude-self of an unsigned $d$-bit integer array of length $n$ under sublinear space must perform two linear passes over the input. More precisely, the algorithm must read at least $n-1$ input…

We present a new algorithm for finding an $\epsilon$-approximate fixed point of an $\ell_\infty$-contracting function $f : [0, 1]^d \rightarrow [0, 1]^d$. Our algorithm is based on the query-efficient algorithm by Chen, Li, and Yannakakis…

We study Euclidean $k$-Means under the Massively Parallel Computation (MPC) model, focusing on the \emph{fully-scalable} setting. Our main result is a fully-scalable $O((\log n/\log\log n)^2)$-approximation in $O(1)$ rounds. Previously,…

Many problems are known to be solvable in subexponential parameterized time when the input graph is planar. The bidimensionality framework of Demaine, Fomin, Hajiaghay, and Thilikos [JACM'05] and the treewidth-pattern-covering approach by…

We study four-cycle counting in arbitrary order graph streams. We present a 3-pass algorithm for $(1+\varepsilon)$-approximating the number of four-cycles using $\widetilde{O}(m/\sqrt{T})$ space, where $m$ is the number of edges and $T$ the…

How to utilize an allocated budget effectively for branding and promotion of a commercial house is an important problem, particularly when multiple advertising media are available. There exist multiple such media, and among them, two…

In this study, we tackle the problem of finding a maximum \emph{co-3-plex}, which is a subset of vertices of an input graph, inducing a subgraph of maximum degree 2. We focus on the class of chordal graphs. By observing that the graph…

The Maximum (Minimum) Leaf Spanning Tree problem asks for a spanning tree with the largest (smallest) number of leaves. As spanning trees are often computed using graph search algorithms, it is natural to restrict this problem to the set of…

We revisit three fundamental problems in algorithms under uncertainty: the Secretary Problem, Prophet Inequality, and Stochastic Probing, each subject to general downward-closed constraints. When elements have binary values, all three…

Randomized greedy algorithms form one of the simplest yet most effective approaches for computing approximate matchings in graphs. In this paper, we focus on the class of vertex-iterative (VI) randomized greedy matching algorithms, which…

Given an unweighted graph $G$, the *minimum $r$-dominating set problem* asks for the smallest-cardinality subset $S$ such that every vertex in $G$ is within radius $r$ of some vertex in $S$. While the $r$-dominating set problem on planar…

Given a text, a query $\mathsf{rank}(q, c)$ counts the number of occurrences of character $c$ among the first $q$ characters of the text. Space-efficient methods to answer these rank queries form an important building block in many succinct…