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For a text given in advance, the substring minimal suffix queries ask to determine the lexicographically minimal non-empty suffix of a substring specified by the location of its occurrence in the text. We develop a data structure answering…
A border of a string is a non-empty proper prefix of the string that is also a suffix. A string is unbordered if it has no border. The longest unbordered factor is a fundamental notion in stringology, closely related to string periodicity.…
In this paper we present an algorithm for enumerating without repetitions all the non-crossing generically minimally rigid bar-and-joint frameworks under edge constraints (also called constrained non-crossing Laman frameworks) on a given…
With the rising popularity of Transformer-based large language models (LLMs), reducing their high inference costs has become a significant research focus. One effective approach is to compress the long input contexts. Existing methods…
We present an $O(\log d + \log\log_{m/n} n)$-time randomized PRAM algorithm for computing the connected components of an $n$-vertex, $m$-edge undirected graph with maximum component diameter $d$. The algorithm runs on an ARBITRARY CRCW…
Min-plus product of two $n\times n$ matrices is a fundamental problem in algorithm research. It is known to be equivalent to APSP, and in general it has no truly subcubic algorithms. In this paper, we focus on the min-plus product on a…
A Wheeler automaton is a finite state automaton whose states admit a total Wheeler order, reflecting the co-lexicographic order of the strings labeling source-to-node paths. A Wheeler language is a regular language admitting an accepting…
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…
The maximum bipartite matching problem is among the most fundamental and well-studied problems in combinatorial optimization. A beautiful and celebrated combinatorial algorithm of Hopcroft and Karp (1973) shows that maximum bipartite…
Low dimensional nonlinear structure abounds in datasets across computer vision and machine learning. Kernelized matrix factorization techniques have recently been proposed to learn these nonlinear structures for denoising, classification,…
Loop transformations are semantics-preserving optimization techniques, widely used to maximize objectives such as parallelism. Despite decades of research, applying the optimal composition of loop transformations remains challenging due to…
What is the time complexity of matrix multiplication of sparse integer matrices with $m_{in}$ nonzeros in the input and $m_{out}$ nonzeros in the output? This paper provides improved upper bounds for this question for almost any choice of…
Indexing highly repetitive texts --- such as genomic databases, software repositories and versioned text collections --- has become an important problem since the turn of the millennium. A relevant compressibility measure for repetitive…
Given two sequences $A[1..n]$ and $B[1..m]$ over a totally ordered alphabet, the \emph{Longest Common Bitonic Subsequence} (LCBS) problem asks for a longest common subsequence that is strictly increasing up to a single peak element and…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
Efficient computation of shortest cycles which form a homology basis under $\mathbb{Z}_2$-additions in a given simplicial complex $\mathcal{K}$ has been researched actively in recent years. When the complex $\mathcal{K}$ is a weighted graph…
This paper studies the problem of enumerating all maximal collinear subsets of size at least three in a given set of $n$ points. An algorithm for this problem, besides solving degeneracy testing and the exact fitting problem, can also help…
Orthogonal time-frequency space (OTFS) scheme, which transforms a time and frequency selective channel into an almost non-selective channel in the delay-Doppler domain, establishes reliable wireless communication for high-speed moving…
We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…
We develop an efficient alternating framework for learning a generalized version of Factorization Machine (gFM) on steaming data with provable guarantees. When the instances are sampled from $d$ dimensional random Gaussian vectors and the…