Related papers: Compact Fenwick trees for dynamic ranking and sele…

The dynamic trees problem is to maintain a tree under edge updates while supporting queries like connectivity queries or path queries. Despite the first data structure for this fundamental problem -- the link-cut tree -- being invented 40…

We present an axiomatic framework for analyzing the algorithmic properties of decision trees. This framework supports the classification of decision tree problems through structural and ancestral constraints within a rigorous mathematical…

We study the problem of designing a \emph{resilient} data structure maintaining a tree under the Faulty-RAM model [Finocchi and Italiano, STOC'04] in which up to $\delta$ memory words can be corrupted by an adversary. Our data structure…

Tree data structures, such as red-black trees, quad trees, treaps, or tries, are fundamental tools in computer science. A classical problem in concurrency is to obtain expressive, efficient, and scalable versions of practical tree data…

We introduce evolving networks where new vertices preferentially connect to the more central parts of a network. This makes such networks compact. Finite networks grown under the preferential compactness mechanism have complex…

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,…

Decision trees are well-known due to their ease of interpretability. To improve accuracy, we need to grow deep trees or ensembles of trees. These are hard to interpret, offsetting their original benefits. Shapley values have recently become…

Learning meaningful topic models with massive document collections which contain millions of documents and billions of tokens is challenging because of two reasons: First, one needs to deal with a large number of topics (typically in the…

Reading comprehension models are based on recurrent neural networks that sequentially process the document tokens. As interest turns to answering more complex questions over longer documents, sequential reading of large portions of text…

Establishing the correspondences between newly acquired points and historically accumulated data (i.e., map) through nearest neighbors search is crucial in numerous robotic applications. However, static tree data structures are inadequate…

This paper introduces the Cartesian Merkle Tree, a deterministic data structure that combines the properties of a Binary Search Tree, a Heap, and a Merkle tree. The Cartesian Merkle Tree supports insertions, updates, and removals of…

Clustering is an important data mining technique that groups similar data records, recently categorical transaction clustering is received more attention. In this research, we study the problem of categorical data clustering for…

As a key ingredient of the DBMS, index plays an important role in the query optimization and processing. However, it is a non-trivial task to apply existing indexes or design new indexes for new applications, where both data distribution…

The classical Fourier transform is, in essence, a way to take data and extract components (in the form of complex exponentials) which are invariant under cyclic shifts. We consider a case in which the components must instead be invariant…

A grammar-compressed ranked tree is represented with a linear space overhead so that a single traversal step, i.e., the move to the parent or the i-th child, can be carried out in constant time. Moreover, we extend our data structure such…

This paper describes a new and purely functional implementation technique of binary heaps. A binary heap is a tree-based data structure that implements priority queue operations (insert, remove, minimum/maximum) and guarantees at worst…

Classification is a common AI problem, and vector search is a typical solution. This transforms a given body of text into a numerical representation, known as an embedding, and modern improvements to vector search focus on optimising speed…

We introduce a batched lazy algorithm for supervised classification using decision trees. It avoids unnecessary visits to irrelevant nodes when it is used to make predictions with either eagerly or lazily trained decision trees. A set of…

This short article presents a new implementation for decision trees. By introducing pre-sorted deques, the leaf-wise greedy tree growing strategy no longer needs to re-sort data at each node, and takes O(kn) time and O(1) extra memory…

Many latent (factorized) models have been proposed for recommendation tasks like collaborative filtering and for ranking tasks like document or image retrieval and annotation. Common to all those methods is that during inference the items…