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We study the density estimation problem defined as follows: given $k$ distributions $p_1, \ldots, p_k$ over a discrete domain $[n]$, as well as a collection of samples chosen from a ``query'' distribution $q$ over $[n]$, output $p_i$ that…

Data Structures and Algorithms · Computer Science 2024-10-31 Anders Aamand , Alexandr Andoni , Justin Y. Chen , Piotr Indyk , Shyam Narayanan , Sandeep Silwal , Haike Xu

Modern tracking technology has made the collection of large numbers of densely sampled trajectories of moving objects widely available. We consider a fundamental problem encountered when analysing such data: Given $n$ polygonal curves $S$…

Computational Geometry · Computer Science 2017-07-18 Peyman Afshani , Anne Driemel

We consider the classical problem of sorting an input array containing $n$ elements, where each element is described with a $k$-bit comparison-key and a $w$-bit payload. A long-standing open problem is whether there exist $(k + w) \cdot o(n…

Data Structures and Algorithms · Computer Science 2020-10-28 Gilad Asharov , Wei-Kai Lin , Elaine Shi

We prove an $\Omega(d \lg n/ (\lg\lg n)^2)$ lower bound on the dynamic cell-probe complexity of statistically $\mathit{oblivious}$ approximate-near-neighbor search ($\mathsf{ANN}$) over the $d$-dimensional Hamming cube. For the natural…

Data Structures and Algorithms · Computer Science 2019-04-11 Kasper Green Larsen , Tal Malkin , Omri Weinstein , Kevin Yeo

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,…

Computational Geometry · Computer Science 2020-02-26 Haitao Wang

We study the fundamental question of how efficiently suffix array entries can be accessed when the array cannot be stored explicitly. The suffix array $SA_T[1..n]$ of a text $T$ of length $n$ encodes the lexicographic order of its suffixes…

Data Structures and Algorithms · Computer Science 2025-10-23 Dominik Kempa , Tomasz Kociumaka

[See the paper for the full abstract.] We show tight upper and lower bounds for time-space trade-offs for the $c$-Approximate Near Neighbor Search problem. For the $d$-dimensional Euclidean space and $n$-point datasets, we develop a data…

Data Structures and Algorithms · Computer Science 2019-10-04 Alexandr Andoni , Thijs Laarhoven , Ilya Razenshteyn , Erik Waingarten

A simple linear search algorithm running in $O(n+mk)$ time is proposed for constructing the lower envelope of $k$ vertices from $m$ monotone polygonal chains in 2D with $n$ vertices in total. This can be applied to output-sensitive…

Computational Geometry · Computer Science 2015-07-07 Daniel Lu

We consider the classical problem of representing a collection of priority queues under the operations \Findmin{}, \Insert{}, \Decrease{}, \Meld{}, \Delete{}, and \Deletemin{}. In the comparison-based model, if the first four operations are…

Data Structures and Algorithms · Computer Science 2011-12-06 Amr Elmasry , Jyrki Katajainen

In the last decades, the necessity to process massive amounts of textual data fueled the development of compressed text indexes: data structures efficiently answering queries on a given text while occupying space proportional to the…

Data Structures and Algorithms · Computer Science 2024-09-24 Dominik Kempa , Tomasz Kociumaka

We prove near-optimal trade-offs for quantifier depth versus number of variables in first-order logic by exhibiting pairs of $n$-element structures that can be distinguished by a $k$-variable first-order sentence but where every such…

Logic in Computer Science · Computer Science 2016-09-02 Christoph Berkholz , Jakob Nordström

We provide a generic technique for constructing families of submodular functions to obtain lower bounds for submodular function minimization (SFM). Applying this technique, we prove that any deterministic SFM algorithm on a ground set of…

Data Structures and Algorithms · Computer Science 2022-07-12 Deeparnab Chakrabarty , Andrei Graur , Haotian Jiang , Aaron Sidford

Given an array A of $n$ elements, we wish to support queries for the most frequent and least frequent element in a subrange $[l, r]$ of $A$. We also wish to support updates that change a particular element at index $i$ or insert/ delete an…

Data Structures and Algorithms · Computer Science 2018-07-12 Hicham El-Zein , Meng He , J. Ian Munro , Bryce Sandlund

We consider the problem of sorting $n$ elements subject to persistent random comparison errors. In this problem, each comparison between two elements can be wrong with some fixed (small) probability $p$, and comparing the same pair of…

Data Structures and Algorithms · Computer Science 2025-08-28 Barbara Geissmann , Stefano Leucci , Chih-Hung Liu , Paolo Penna

We consider the $(1+\epsilon)$-approximate nearest neighbor search problem: given a set $X$ of $n$ points in a $d$-dimensional space, build a data structure that, given any query point $y$, finds a point $x \in X$ whose distance to $y$ is…

Data Structures and Algorithms · Computer Science 2018-07-03 Piotr Indyk , Tal Wagner

Learned top-K search is a promising approach for serving vector queries with both high accuracy and performance. However, current models trained for a specific K value fail to generalize to real-world multi-K queries: they suffer from…

Let $\D = $$ \{d_1,d_2,...d_D\}$ be a given set of $D$ string documents of total length $n$, our task is to index $\D$, such that the $k$ most relevant documents for an online query pattern $P$ of length $p$ can be retrieved efficiently. We…

Data Structures and Algorithms · Computer Science 2012-04-03 Wing-Kai Hon , Rahul Shah , Sharma V. Thankachan

We tackle the problems of computing the rightmost variant of the Lempel-Ziv factorizations in the online/sliding model. Previous best bounds for this problem are O(n log n) time with O(n) space, due to Amir et al. [IPL 2002] for the online…

Data Structures and Algorithms · Computer Science 2024-08-07 Wataru Sumiyoshi , Takuya Mieno , Shunsuke Inenaga

In this paper, we study top-$k$ aggregate (or group) nearest neighbor queries using the weighted SUM operator under the $L_1$ metric in the plane. Given a set $P$ of $n$ points, for any query consisting of a set $Q$ of $m$ weighted points…

Computational Geometry · Computer Science 2014-12-02 Haitao Wang , Wuzhou Zhang

We present the first in-place algorithm for sorting an array of size n that performs, in the worst case, at most O(n log n) element comparisons and O(n) element transports. This solves a long-standing open problem, stated explicitly, e.g.,…

Data Structures and Algorithms · Computer Science 2007-05-23 Gianni Franceschini , Viliam Geffert