Related papers: A Sierpinski Triangle Data Structure for Efficient…
Supervised hashing aims to map the original features to compact binary codes that are able to preserve label based similarity in the Hamming space. Non-linear hash functions have demonstrated the advantage over linear ones due to their…
We present the \crprecis structure, that is a general-purpose, deterministic and sub-linear data structure for summarizing \emph{update} data streams. The \crprecis structure yields the \emph{first deterministic sub-linear space/time…
We present a triangle of connections between the Sierpinski triangle, the sum-of-digits function, and the Binomial Theorem via a one-parameter family of Sierpinski matrices, which encodes a digital version of the Binomial Theorem.
The three-in-a-tree problem is to determine if a simple undirected graph contains an induced subgraph which is a tree connecting three given vertices. Based on a beautiful characterization that is proved in more than twenty pages,…
We propose a new outline for adaptive dictionary learning methods for sparse encoding based on a hierarchical clustering of the training data. Through recursive application of a clustering method, the data is organized into a binary…
In this paper, we provide new insights and analysis for the two elementary tree-based data structures - the AVL tree and binary heap. We presented two simple properties that gives a more direct way of relating the size of an AVL tree and…
The problem of {\em efficiently} finding the best match for a query in a given set with respect to the Euclidean distance or the cosine similarity has been extensively studied in literature. However, a closely related problem of efficiently…
This paper introduces a data structure, called simplex tree, to represent abstract simplicial complexes of any dimension. All faces of the simplicial complex are explicitly stored in a trie whose nodes are in bijection with the faces of the…
Indexes facilitate efficient querying when the selection predicate is on an indexed key. As a result, when loading data, if we anticipate future selective (point or range) queries, we typically maintain an index that is gradually populated…
We introduce a new metric of match, called Cartesian tree matching, which means that two strings match if they have the same Cartesian trees. Based on Cartesian tree matching, we define single pattern matching for a text of length n and a…
Net-trees are a general purpose data structure for metric data that have been used to solve a wide range of algorithmic problems. We give a simple randomized algorithm to construct net-trees on doubling metrics using $O(n\log n)$ time in…
We present bundled references, a new building block to provide linearizable range query operations for highly concurrent lock-based linked data structures. Bundled references allow range queries to traverse a path through the data structure…
We give a new successor data structure which improves upon the index size of the P\v{a}tra\c{s}cu-Thorup data structures, reducing the index size from $O(n w^{4/5})$ bits to $O(n \log w)$ bits, with optimal probe complexity. Alternatively,…
Deep neural networks (DNNs) and decision trees (DTs) are both state-of-the-art classifiers. DNNs perform well due to their representational learning capabilities, while DTs are computationally efficient as they perform inference along one…
Information, stored or transmitted in digital form, is often structured. Individual data records are usually represented as hierarchies of their elements. Together, records form larger structures. Information processing applications have to…
Maintaining an archive of all non-dominated points is a standard task in multi-objective optimization. Sometimes it is sufficient to store all evaluated points and to obtain the non-dominated subset in a post-processing step. Alternatively…
Tree-based data structures are ubiquitous across applications. Therefore, a multitude of different tree implementations exist. However, while these implementations are diverse, they share a tree structure as the underlying data structure.…
We show that the problem of constructing tree-structured descriptions of data layouts that are optimal with respect to space or other criteria from given sequences of displacements, can be solved in polynomial time. The problem is relevant…
This paper presents a new algorithm for the fast, shared memory, multi-core computation of augmented contour trees on triangulations. In contrast to most existing parallel algorithms our technique computes augmented trees, enabling the full…
Tree-structured neural networks exploit valuable syntactic parse information as they interpret the meanings of sentences. However, they suffer from two key technical problems that make them slow and unwieldy for large-scale NLP tasks: they…