数据结构与算法
In this work we revisit the arithmetic and bit complexity of Hermitian eigenproblems. Recently, [BGVKS, FOCS 2020] proved that a (non-Hermitian) matrix can be diagonalized with a randomized algorithm in $O(n^{\omega}\log^2(n/\epsilon))$…
We propose a randomized multiplicative weight update (MWU) algorithm for $\ell_{\infty}$ regression that runs in $\widetilde{O}\left(n^{2+1/22.5} \text{poly}(1/\epsilon)\right)$ time when $\omega = 2+o(1)$, improving upon the previous best…
Queue length monitoring is a commonly arising problem in numerous applications such as queue management systems, scheduling, and traffic monitoring. Motivated by such applications, we formulate a queue monitoring problem, where there is a…
The notion of a (polynomial) kernelization from parameterized complexity is a well-studied model for efficient preprocessing for hard computational problems. By now, it is quite well understood which parameterized problems do or…
Given a directed graph $G$, a transitive reduction $G^t$ of $G$ (first studied by Aho, Garey, Ullman [SICOMP `72]) is a minimal subgraph of $G$ that preserves the reachability relation between every two vertices in $G$. In this paper, we…
The Fixed Charge Transportation (FCT) problem models transportation scenarios where we need to send a commodity from $n$ sources to $m$ sinks, and the cost of sending a commodity from a source to a sink consists of a linear component and a…
We consider a basic computational task of finding $s$ planted rank-1 $m \times n$ matrices in a linear subspace $\mathcal{U} \subseteq \mathbb{R}^{m \times n}$ where $\dim(\mathcal{U}) = R \ge s$. The work of Johnston-Lovitz-Vijayaraghavan…
We present an optimal oracle for answering connectivity queries in undirected graphs in the presence of at most three vertex failures. Specifically, we show that we can process a graph $G$ in $O(n+m)$ time, in order to build a data…
In the \textsc{Geodetic Set} problem, the input consists of a graph $G$ and a positive integer $k$. The goal is to determine whether there exists a subset $S$ of vertices of size $k$ such that every vertex in the graph is included in a…
The classical rank aggregation problem seeks to combine a set X of n permutations into a single representative "consensus" permutation. In this paper, we investigate two fundamental rank aggregation tasks under the well-studied Ulam metric:…
The $k$-center problem is a fundamental optimization problem with numerous applications in machine learning, data analysis, data mining, and communication networks. The $k$-center problem has been extensively studied in the classical…
There has recently been significant interest in fault tolerant spanners, which are spanners that still maintain their stretch guarantees after some nodes or edges fail. This work has culminated in an almost complete understanding of the…
Fitting distances to tree metrics and ultrametrics are two widely used methods in hierarchical clustering, primarily explored within the context of numerical taxonomy. Given a positive distance function…
In this paper, we present a general framework for efficiently computing diverse solutions to combinatorial optimization problems. Given a problem instance, the goal is to find $k$ solutions that maximize a specified diversity measure; the…
The current landscape of balanced graph partitioning is divided into high-quality but expensive multilevel algorithms and cheaper approaches with linear running time, such as single-level algorithms and streaming algorithms. We demonstrate…
Algorithms in the data stream model use $O(polylog(N))$ space to compute some property of an input of size $N$, and many of these algorithms are implemented and used in practice. However, sketching algorithms in the graph semi-streaming…
In the knapsack problems with neighborhood constraints that were studied before, the input is a graph $\mathcal{G}$ on a set $\mathcal{V}$ of items, each item $v \in \mathcal{V}$ has a weight $w_v$ and profit $p_v$, the size $s$ of the…
We study a fundamental stochastic selection problem involving $n$ independent random variables, each of which can be queried at some cost. Given a tolerance level $\delta$, the goal is to find a value that is $\delta$-approximately minimum…
We provide tools for sharing sensitive data when the data curator does not know in advance what questions an (untrusted) analyst might ask about the data. The analyst can specify a program that they want the curator to run on the dataset.…
In a temporal graph the edge set dynamically changes over time according to a set of time-labels associated with each edge that indicates at which time-steps the edge is available. Two vertices are connected if there is a path connecting…