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Mixed-integer linear programming (MILP) is at the core of many advanced algorithms for solving fundamental problems in combinatorial optimization. The complexity of solving MILPs directly correlates with their support size, which is the…
Mixed Integer Programming (MIP) is one of the most widely used modeling techniques for combinatorial optimization problems. In many applications, a similar MIP model is solved on a regular basis, maintaining remarkable similarities in model…
Efficient indexing and searching of high dimensional data has been an area of active research due to the growing exploitation of high dimensional data and the vulnerability of traditional search methods to the curse of dimensionality. This…
A common problem in applied mathematics is to find a function in a Hilbert space with prescribed best approximations from a finite number of closed vector subspaces. In the present paper we study the question of the existence of solutions…
Neural embedding models are extensively employed in the table union search problem, which aims to find semantically compatible tables that can be merged with a given query table. In particular, multi-vector models, which represent a table…
Content addressable memory (CAM) is widely used in associative search tasks for its highly parallel pattern matching capability. To accommodate the increasingly complex and data-intensive pattern matching tasks, it is critical to keep…
We study the Closest Pair Problem in Hamming metric, which asks to find the pair with the smallest Hamming distance in a collection of binary vectors. We give a new randomized algorithm for the problem on uniformly random input…
In millimeter wave cellular communication, fast and reliable beam alignment via beam training is crucial to harvest sufficient beamforming gain for the subsequent data transmission. In this paper, we establish fundamental limits in…
Maximum inner product search (MIPS) over dense and sparse vectors have progressed independently in a bifurcated literature for decades; the latter is better known as top-$k$ retrieval in Information Retrieval. This duality exists because…
Learned sparse representations form an attractive class of contextual embeddings for text retrieval. That is so because they are effective models of relevance and are interpretable by design. Despite their apparent compatibility with…
We describe an algorithm to find maximal exact matches (MEMs) among HiFi reads with homopolymer errors. The main novelty in our work is that we resort to run-length compression to help deal with errors. Our method receives as input a…
We introduce a new, practical method for conducting an exact search in a uni- and bidirectional FM index in $O(1)$ time per step while using $O(\log \sigma * n) + o(\log \sigma * \sigma * n)$ bits of space. This is done by replacing the…
Inverted file structure is a common technique for accelerating dense retrieval. It clusters documents based on their embeddings; during searching, it probes nearby clusters w.r.t. an input query and only evaluates documents within them by…
Many modern sequence alignment tools implement fast string matching using the space efficient data structure called FM-index. The succinct nature of this data structure presents unique challenges for the algorithm designers. In this paper,…
Approximate $k$ nearest neighbor (AKNN) search in high-dimensional space is a foundational problem in vector databases with widespread applications. Among the numerous AKNN indexes, Proximity Graph-based indexes achieve state-of-the-art…
Given a bipartite graph, the maximum balanced biclique (\textsf{MBB}) problem, discovering a mutually connected while equal-sized disjoint sets with the maximum cardinality, plays a significant role for mining the bipartite graph and has…
Similarity search finds objects that are similar to a given query object based on a similarity metric. As the amount and variety of data continue to grow, similarity search in metric spaces has gained significant attention. Metric spaces…
We introduce the natural notion of a matching frame in a $2$-dimensional string. A matching frame in a $2$-dimensional $n\times m$ string $M$, is a rectangle such that the strings written on the horizontal sides of the rectangle are…
Availability of research datasets is keystone for health and life science study reproducibility and scientific progress. Due to the heterogeneity and complexity of these data, a main challenge to be overcome by research data management…
Mixed-integer programming (MIP) is a well-established framework for computer-aided molecular design (CAMD). By precisely encoding the molecular space and score functions, e.g., a graph neural network, the molecular design problem is…