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This paper introduces k-splits, an improved hierarchical algorithm based on k-means to cluster data without prior knowledge of the number of clusters. K-splits starts from a small number of clusters and uses the most significant data…

Motivation: Seed filtering is critical in DNA read mapping, a process where billions of DNA fragments (reads) sampled from a donor are mapped onto a reference genome to identify genomic variants of the donor. Read mappers 1) quickly…

In this paper, we first propose a new iterative algorithm, called the K-sets+ algorithm for clustering data points in a semi-metric space, where the distance measure does not necessarily satisfy the triangular inequality. We show that the…

We consider the problem of testing for a difference in means between clusters of observations identified via k-means clustering. In this setting, classical hypothesis tests lead to an inflated Type I error rate. To overcome this problem, we…

This note describes a new efficient bit-slice implementation DenseQMC of the Quine-McCluskey algorithm for finding all prime implicants of a Boolean function in the dense case. It is practically feasible for n <= 23 when run on a common…

$k$-means++ is an important algorithm for choosing initial cluster centers for the $k$-means clustering algorithm. In this work, we present a new algorithm that can solve the $k$-means++ problem with nearly optimal running time. Given $n$…

Recurrent LLM architectures have emerged as a promising approach for improving reasoning, as they enable multi-step computation in the embedding space without generating intermediate tokens. Models such as Ouro perform reasoning by…

Real world datasets are sparse, dirty and contain hundreds of items. In such situations, discovering interesting rules (results) using traditional frequent itemset mining approach by specifying a user defined input support threshold is not…

High read and write performance is important for generic key-value stores, which are foundational to modern applications and databases. Yet, achieving high performance for mixed and dynamic workloads is challenging due to fundamental…

Filters such as Bloom, quotient, and cuckoo filters are fundamental building blocks providing space-efficient approximate set membership testing. However, many applications need to associate small values with keys-functionality that filters…

Kernel power $k$-means (KPKM) leverages a family of means to mitigate local minima issues in kernel $k$-means. However, KPKM faces two key limitations: (1) the computational burden of the full kernel matrix restricts its use on extensive…

Quantum memories are a fundamental of any global-scale quantum Internet, high-performance quantum networking and near-term quantum computers. A main problem of quantum memories is the low retrieval efficiency of the quantum systems from the…

We propose a new clustering algorithm that is robust to the presence of outliers in the dataset. We perform Lloyd-type iterations with robust estimates of the centroids. More precisely, we build on the idea of median-of-means statistics to…

The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples…

Catastrophic forgetting, the phenomenon of forgetting previously learned tasks when learning a new one, is a major hurdle in developing continual learning algorithms. A popular method to alleviate forgetting is to use a memory buffer, which…

Quantum machine learning is one of the most promising applications of a full-scale quantum computer. Over the past few years, many quantum machine learning algorithms have been proposed that can potentially offer considerable speedups over…

Being robust to the presence of outliers is crucial for applying clustering algorithms in practice. In the $\textit{robust $k$-Means}$ problem (i.e., $k$-Means with outliers), the goal is to remove $z$ outliers and minimize the $k$-Means…

Bloom filters are a fundamental data structure for approximate membership queries, with applications ranging from data analytics to databases and genomics. Several variants have been proposed to accommodate parallel architectures. GPUs,…

Cumulative memory -- the sum of space used per step over the duration of a computation -- is a fine-grained measure of time-space complexity that was introduced to analyze cryptographic applications like password hashing. It is a more…

Memory and computation remain core bottlenecks in long-horizon LLM inference due to the quadratic cost of self-attention and the ever-growing key-value (KV) cache. Existing strategies for memory-bounded inference, such as quantization,…