Related papers: Heavy hitters via cluster-preserving clustering

Sorting has a natural generalization where the input consists of: (1) a ground set $X$ of size $n$, (2) a partial oracle $O_P$ specifying some fixed partial order $P$ on $X$ and (3) a linear oracle $O_L$ specifying a linear order $L$ that…

In this paper, we first consider the subpath convex hull query problem: Given a simple path $\pi$ of $n$ vertices, preprocess it so that the convex hull of any query subpath of $\pi$ can be quickly obtained. Previously, Guibas, Hershberger,…

We develop dynamic data structures for maintaining a hierarchical k-center clustering when the points come from a discrete space $\{1,\ldots,\Delta\}^d$. Our first data structure is for the low dimensional setting, i.e., d is a constant,…

We give optimal sorting algorithms in the evolving data framework, where an algorithm's input data is changing while the algorithm is executing. In this framework, instead of producing a final output, an algorithm attempts to maintain an…

We present a non-algebraic, locality-preserving framework for triangle detection in worst-case sparse graphs. Our algorithm processes the graph in $O(\log n)$ independent layers and partitions incident edges into prefix-based classes where…

We discuss the problem of counting distinct elements in a stream. A stream is usually considered as a sequence of elements that come one at a time. An exact solution to the problem requires memory space of the size of the stream. For many…

As long-context inference becomes central to large language models (LLMs), attention over growing key-value caches emerges as a dominant decoding bottleneck, motivating sparse attention for scalable inference. Fixed-budget top-k sparse…

We propose a technique called Rotate-and-Kill for solving the polygon inclusion and circumscribing problems. By applying this technique, we obtain $O(n)$ time algorithms for computing (1) the maximum area triangle in a given $n$-sided…

We study the Multiple Cluster Scheduling problem and the Multiple Strip Packing problem. For both problems, there is no algorithm with approximation ratio better than $2$ unless $P = NP$. In this paper, we present an algorithm with…

Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data. Despite several appealing properties, incorporating PDs in learning pipelines can be challenging because their natural geometry is not…

We show an $\tilde{O}(n^{p/(p+2)})$-round algorithm in the \congest model for \emph{listing} of $K_p$ (a clique with $p$ nodes), for all $p =4, p\geq 6$. For $p = 5$, we show an $\tilde{O}(n^{3/4})$-round algorithm. For $p=4$ and $p=5$, our…

Hankel matrices are an important class of highly-structured matrices, arising across computational mathematics, engineering, and theoretical computer science. It is well-known that positive semidefinite (PSD) Hankel matrices are always…

We study the problem of computing a convex region with bounded area and diameter that contains the maximum number of points from a given point set $P$. We show that this problem can be solved in $O(n^6k)$ time and $O(n^3k)$ space, where $n$…

The study of optimal decision trees has gained increasing attention in recent years; however, despite substantial progress, it still suffers from two major challenges: First, trees constructed by existing optimal decision tree (ODT)…

In many applications of clustering (for example, ontologies or clusterings of animal or plant species), hierarchical clusterings are more descriptive than a flat clustering. A hierarchical clustering over $n$ elements is represented by a…

Large Language Models (LLMs), despite their recent impressive accomplishments, are notably cost-prohibitive to deploy, particularly for applications involving long-content generation, such as dialogue systems and story writing. Often, a…

We study pseudo-polynomial time algorithms for the fundamental \emph{0-1 Knapsack} problem. In terms of $n$ and $w_{\max}$, previous algorithms for 0-1 Knapsack have cubic time complexities: $O(n^2w_{\max})$ (Bellman 1957), $O(nw_{\max}^2)$…

Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately,…

Weighted sampling is a fundamental tool in data analysis and machine learning pipelines. Samples are used for efficient estimation of statistics or as sparse representations of the data. When weight distributions are skewed, as is often the…

Warehouses are nowadays the scene of complex logistic problems integrating different decision layers. This paper addresses the Joint Order Batching, Picker Routing and Sequencing Problem with Deadlines (JOBPRSP-D) in rectangular warehouses.…