数据结构与算法

The graph reconstruction problem has been extensively studied under various query models. In this paper, we propose a new query model regarding the number of connected components, which is one of the most basic and fundamental graph…

We consider the basic problem of learning an unknown partition of $n$ elements into at most $k$ sets using simple queries that reveal information about a small subset of elements. Our starting point is the well-studied pairwise same-set…

We present a nearly linear work parallel algorithm for approximating the Held-Karp bound for the Metric TSP problem. Given an edge-weighted undirected graph $G=(V,E)$ on $m$ edges and $\epsilon>0$, it returns a $(1+\epsilon)$-approximation…

The streaming max-min diversification problem concerns the selection of a limited and diverse sample of items out of a data stream of known finite length. The objective to be maximized is the minimum distance among any pair of selected…

In the problem Fault-Tolerant Path (FTP), we are given an edge-weighted directed graph G = (V, E), a subset U \subseteq E of vulnerable edges, two vertices s, t \in V, and integers k and \ell. The task is to decide whether there exists a…

Dynamic tree data structures maintain a forest while supporting insertion and deletion of edges and a broad set of queries in $O(\log n)$ time per operation. Such data structures are at the core of many modern algorithms. Recent work has…

The problem of identifying the maximum edge biclique in bipartite graphs has attracted considerable attention in bipartite graph analysis, with numerous real-world applications such as fraud detection, community detection, and online…

Hypergraphs provide a natural representation for many-to-many relationships in data-intensive applications, yet their scalability is often hindered by high memory consumption. While prior work has improved computational efficiency, reducing…

A computational bottleneck in current Vector-Symbolic Architectures (VSAs) is the ``clean-up'' step, which decodes the noisy vectors retrieved from the architecture. Clean-up typically compares noisy vectors against a ``codebook'' of…

Prophet inequalities are a central object of study in optimal stopping theory. In the iid model, a gambler sees values in an online fashion, sampled independently from a given distribution. Upon observing each value, the gambler either…

The selection of influential billboard slots remains an important problem in billboard advertisements. Existing studies on this problem have not considered the case of context-specific influence probability. To bridge this gap, in this…

We provide a more efficient algorithm for computing the Rand Index when the data cluster comes from a change-point detection problem. Given $N$ data points and two clusterings of size $r$ and $s$, the algorithm runs on $O(r+s)$ time…

Inspired by the famous Target Set Selection problem, we propose a new discrete model to simultaneously spread two opinions within a social network and perform an initial study of its complexity. Here, we are given a social network, a…

When the Mersenne Twister made his first appearance in 1997 it was a powerful example of how linear maps on $\mathbf F_2$ could be used to generate pseudorandom numbers. In particular, the easiness with which generators with long periods…

We consider the Global Minimum Vertex-Cut problem: given an undirected vertex-weighted graph $G$, compute a minimum-weight subset of its vertices whose removal disconnects $G$. The problem is closely related to Global Minimum Edge-Cut,…

Word Break is a prototypical factorization problem in string processing: Given a word $w$ of length $N$ and a dictionary $\mathcal{D} = \{d_1, d_2, \ldots, d_{K}\}$ of $K$ strings, determine whether we can partition $w$ into words from…

In this work, we study the relative hardness of fundamental problems with state-of-the-art word RAM algorithms that take $O(n\sqrt{\log n})$ time for instances described in $\Theta(n)$ machine words ($\Theta(n\log n)$ bits). This complexity…

Lempel-Ziv (LZ77) factorization is a fundamental problem in string processing: Greedily partition a given string $T$ from left to right into blocks (called phrases) so that each phrase is either the leftmost occurrence of a letter or the…

The "ordered set" abstract data type with operations "insert", "erase", "find", "min", "max", "next" and "prev" is ubiquitous in computer science. It is usually implemented with red-black trees, $B$-trees, or $B^+$-trees. We present our…

We define and study a spectral recombination algorithm, SpecReCom, for partitioning a graph into a given number of connected parts. It is straightforward to introduce additional constraints such as the requirement that the weight (or number…