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We devise a data structure that can answer shortest path queries for two query points in a polygonal domain $P$ on $n$ vertices. For any $\varepsilon > 0$, the space complexity of the data structure is $O(n^{10+\varepsilon })$ and queries…

Computational Geometry · Computer Science 2024-02-22 Sarita de Berg , Tillmann Miltzow , Frank Staals

Many modern multiclass and multilabel problems are characterized by increasingly large output spaces. For these problems, label embeddings have been shown to be a useful primitive that can improve computational and statistical efficiency.…

Machine Learning · Computer Science 2015-04-01 Paul Mineiro , Nikos Karampatziakis

We show that any embedding of a planar graph can be encoded succinctly while efficiently answering a number of topological queries near-optimally. More precisely, we build on a succinct representation that encodes an embedding of $m$ edges…

Data Structures and Algorithms · Computer Science 2021-12-14 José Fuentes-Sepúlveda , Gonzalo Navarro , Diego Seco

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

A class of graphs admits an adjacency labeling scheme of size $b(n)$, if the vertices in each of its $n$-vertex graphs can be assigned binary strings (called labels) of length $b(n)$ so that the adjacency of two vertices can be determined…

Combinatorics · Mathematics 2024-02-21 Édouard Bonnet , Julien Duron , John Sylvester , Viktor Zamaraev , Maksim Zhukovskii

Classification and clustering are both important topics in statistical learning. A natural question herein is whether predefined classes are really different from one another, or whether clusters are really there. Specifically, we may be…

Machine Learning · Statistics 2015-09-22 Qiyi Lu , Xingye Qiao

We solve an open problem related to an optimal encoding of a straight line program (SLP), a canonical form of grammar compression deriving a single string deterministically. We show that an information-theoretic lower bound for representing…

Data Structures and Algorithms · Computer Science 2013-06-18 Yasuo Tabei , Yoshimasa Takabatake , Hiroshi Sakamoto

Motivated by the problem of maintaining data structures for a large sets of points that are evolving over the course of time, we consider the problem of maintaining a set of labels assigned to the vertices of a tree, where the locations of…

Data Structures and Algorithms · Computer Science 2022-08-24 Aditya Acharya , David M. Mount

We study the simultaneous embeddability of a pair of partitions of the same underlying set into disjoint blocks. Each element of the set is mapped to a point in the plane and each block of either of the two partitions is mapped to a region…

Computational Geometry · Computer Science 2014-08-27 Jan Christoph Athenstädt , Tanja Hartmann , Martin Nöllenburg

Fully indexable dictionaries (FID) store sets of integer keys while supporting rank/select queries. They serve as basic building blocks in many succinct data structures. Despite the great importance of FIDs, no known FID is succinct with…

Data Structures and Algorithms · Computer Science 2025-04-29 Jingxun Liang , Renfei Zhou

Encoding data structures store enough information to answer the queries they are meant to support but not enough to recover their underlying datasets. In this paper we give the first encoding data structure for the challenging problem of…

Data Structures and Algorithms · Computer Science 2017-02-21 Travis Gagie , Giovanni Manzini , Rossano Venturini

We study an extension of active learning in which the learning algorithm may ask the annotator to compare the distances of two examples from the boundary of their label-class. For example, in a recommendation system application (say for…

Machine Learning · Computer Science 2017-06-05 Daniel M. Kane , Shachar Lovett , Shay Moran , Jiapeng Zhang

We describe a data structure that stores a string $S$ in space similar to that of its Lempel-Ziv encoding and efficiently supports access, rank and select queries. These queries are fundamental for implementing succinct and compressed data…

Data Structures and Algorithms · Computer Science 2014-12-03 Djamal Belazzougui , Travis Gagie , Paweł Gawrychowski , Juha Kärkkäinen , Alberto Ordóñez , Simon J. Puglisi , Yasuo Tabei

For every fixed $d \in \mathbb{N}$, we design a data structure that represents a binary $n \times n$ matrix that is $d$-twin-ordered. The data structure occupies $O_d(n)$ bits, which is the least one could hope for, and can be queried for…

Data Structures and Algorithms · Computer Science 2021-10-18 Michał Pilipczuk , Marek Sokołowski , Anna Zych-Pawlewicz

We revisit the range minimum query problem and present a new O(n)-space data structure that supports queries in O(1) time. Although previous data structures exist whose asymptotic bounds match ours, our goal is to introduce a new solution…

Data Structures and Algorithms · Computer Science 2011-09-22 Stephane Durocher

In a setting where segmentation models have to be built for multiple datasets, each with its own corresponding label set, a straightforward way is to learn one model for every dataset and its labels. Alternatively, multi-task architectures…

Computer Vision and Pattern Recognition · Computer Science 2024-11-19 Deepa Anand , Bipul Das , Vyshnav Dangeti , Antony Jerald , Rakesh Mullick , Uday Patil , Pakhi Sharma , Prasad Sudhakar

We consider the problem of encoding two-dimensional arrays, whose elements come from a total order, for answering \topk{} queries. The aim is to obtain encodings that use space close to the information-theoretic lower bound, which can be…

Data Structures and Algorithms · Computer Science 2021-07-13 Seungbum Jo , Srinivasa Rao Satti

Under the word RAM model, we design three data structures that can be constructed in $O(n\sqrt{\lg n})$ time over $n$ points in an $n \times n$ grid. The first data structure is an $O(n\lg^{\epsilon} n)$-word structure supporting orthogonal…

Data Structures and Algorithms · Computer Science 2020-06-23 Younan Gao , Meng He , Yakov Nekrich

Active learning is commonly used to train label-efficient models by adaptively selecting the most informative queries. However, most active learning strategies are designed to either learn a representation of the data (e.g., embedding or…

Machine Learning · Computer Science 2022-02-07 Namrata Nadagouda , Austin Xu , Mark A. Davenport

Given a vertex-labeled graph, each vertex $v$ is attached with a label from a set of labels. The vertex-label query desires the length of the shortest path from the given vertex to the set of vertices with the given label. We show how to…

Data Structures and Algorithms · Computer Science 2012-02-01 Mingfei Li , Christoffer Ma , Li Ning