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We initiate the study on fault-tolerant spanners in hypergraphs and develop fast algorithms for their constructions. A fault-tolerant (FT) spanner preserves approximate distances under network failures, often used in applications like…
The key problem in multivariate time series (MTS) analysis and forecasting aims to disclose the underlying couplings between variables that drive the co-movements. Considerable recent successful MTS methods are built with graph neural…
Understanding and explaining the predictions of Graph Neural Networks (GNNs), is crucial for enhancing their safety and trustworthiness. Subgraph-level explanations are gaining attention for their intuitive appeal. However, most existing…
In the past thirty years, numerous algorithms for building the suffix array of a string have been proposed. In 2021, the notion of suffix array was extended from strings to DFAs, and it was shown that the resulting data structure can be…
Electroencephalography (EEG) signals provide critical insights for applications in disease diagnosis and healthcare. However, the scarcity of labeled EEG data poses a significant challenge. Foundation models offer a promising solution by…
We give an algorithmic and lower-bound framework that facilitates the construction of subexponential algorithms and matching conditional complexity bounds. It can be applied to intersection graphs of similarly-sized fat objects, yielding…
Protein structure prediction often hinges on multiple sequence alignments (MSAs), which underperform on low-homology and orphan proteins. We introduce PLAME, a lightweight MSA design framework that leverages evolutionary embeddings from…
We study \emph{local computation algorithms (LCAs)} for constructing spanning trees. In this setting, the goal is to locally determine, for each edge $ e \in E $, whether it belongs to a spanning tree $ T $ of the input graph $ G $, where $…
We consider the problem of compactly representing the Depth First Search (DFS) tree of a given undirected or directed graph having $n$ vertices and $m$ edges while supporting various DFS related queries efficiently in the RAM with…
We investigate the limits of one of the fundamental ideas in data structures: fractional cascading. This is an important data structure technique to speed up repeated searches for the same key in multiple lists and it has numerous…
The suffix array is a fundamental data structure for many applications that involve string searching and data compression. Designing time/space-efficient suffix array construction algorithms has attracted significant attention and…
We deal with the problem of maintaining the suffix tree indexing structure for a fully-online collection of multiple strings, where a new character can be prepended to any string in the collection at any time. The only previously known…
Given a threshold $L$ and a set $\mathcal{R} = \{R_1, \ldots, R_m\}$ of $m$ haplotype sequences, each having length $n$, the minimum segmentation problem for founder reconstruction is to partition the sequences into disjoint segments…
We give the first almost-linear time algorithm for computing the \emph{maximal $k$-edge-connected subgraphs} of an undirected unweighted graph for any constant $k$. More specifically, given an $n$-vertex $m$-edge graph $G=(V,E)$ and a…
For an arbitrary undirected simple graph G with m edges, we give an algorithm with running time O(m^4 |L|^2) to generate the set L of all minimal edge dominating sets of G. For bipartite graphs we obtain a better result; we show that their…
In this paper we describe an algorithm that embeds a graph metric $(V,d_G)$ on an undirected weighted graph $G=(V,E)$ into a distribution of tree metrics $(T,D_T)$ such that for every pair $u,v\in V$, $d_G(u,v)\leq d_T(u,v)$ and…
Pattern matching queries on strings can be solved in linear time by Knuth-Morris-Pratt (KMP) algorithm. In 1973, Weiner introduced the suffix tree of a string [FOCS 1973] and showed that the seemingly more difficult problem of computing…
In a \emph{weighted sequence}, for every position of the sequence and every letter of the alphabet a probability of occurrence of this letter at this position is specified. Weighted sequences are commonly used to represent imprecise or…
The field of succinct data structures has flourished over the last 16 years. Starting from the compressed suffix array (CSA) by Grossi and Vitter (STOC 2000) and the FM-index by Ferragina and Manzini (FOCS 2000), a number of generalizations…
We study the problems of finding a minimum cycle basis (a minimum weight set of cycles that form a basis for the cycle space) and a minimum homology basis (a minimum weight set of cycles that generates the $1$-dimensional…