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'Tree-based' phylogenetic networks proposed by Francis and Steel have attracted much attention of theoretical biologists in the last few years. At the heart of the definitions of tree-based phylogenetic networks is the notion of 'support…
Augmented B-trees (aB-trees) are a broad class of data structures. The seminal work "succincter" by Patrascu showed that any aB-tree can be stored using only two bits of redundancy, while supporting queries to the tree in time proportional…
The active field of Functional Data Analysis (about understanding the variation in a set of curves) has been recently extended to Object Oriented Data Analysis, which considers populations of more general objects. A particularly challenging…
In this paper we face the problem of representation of functional data with the tools of algebraic topology. We represent functions by means of merge trees, which, like the more commonly used persistence diagrams, are invariant under…
Navarro and Sadakane [TALG 2014] gave a dynamic succinct data structure for storing an ordinal tree. The structure supports tree queries in either $O(\log n/\log\log n)$ or $O(\log n)$ time, and insertion or deletion of a single node in…
Tucker decomposition has been widely used in a variety of applications to obtain latent factors of tensor data. In these applications, a common need is to compute Tucker decomposition for a given time range. Furthermore, real-world tensor…
Variable trees are a new method for the exploration of discrete multivariate data. They display nested subsets and corresponding frequencies and percentages. Manual calculation of these quantities can be laborious, especially when there are…
Dynamic trees are a well-studied and fundamental building block of dynamic graph algorithms dating back to the seminal work of Sleator and Tarjan [STOC'81, (1981), pp. 114-122]. The problem is to maintain a tree subject to online edge…
In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species $X$; these relationships are often depicted via a phylogenetic tree -- a tree having its leaves univocally labeled by elements of $X$…
Linear tree constraints were introduced by Hofmann and Rodriguez in the context of amortized resource analysis for object oriented programs. More precisely, they gave a reduction from inference of resource types to constraint solving. Thus,…
Tree-structured neural networks encode a particular tree geometry for a sentence in the network design. However, these models have at best only slightly outperformed simpler sequence-based models. We hypothesize that neural sequence models…
We propose to compose dynamic tree structures that place the objects in an image into a visual context, helping visual reasoning tasks such as scene graph generation and visual Q&A. Our visual context tree model, dubbed VCTree, has two key…
The dynamic trees problem is to maintain a forest subject to edge insertions and deletions while facilitating queries such as connectivity, path weights, and subtree weights. Dynamic trees are a fundamental building block of a large number…
The forest matrix plays a crucial role in network science, opinion dynamics, and machine learning, offering deep insights into the structure of and dynamics on networks. In this paper, we study the problem of querying entries of the forest…
We consider succinct data structures for representing a set of $n$ horizontal line segments in the plane given in rank space to support \emph{segment access}, \emph{segment selection}, and \emph{segment rank} queries. A segment access query…
Tree-structured neural networks have proven to be effective in learning semantic representations by exploiting syntactic information. In spite of their success, most existing models suffer from the underfitting problem: they recursively use…
An indexed sequence of strings is a data structure for storing a string sequence that supports random access, searching, range counting and analytics operations, both for exact matches and prefix search. String sequences lie at the core of…
We present a new universal source code for distributions of unlabeled binary and ordinal trees that achieves optimal compression to within lower order terms for all tree sources covered by existing universal codes. At the same time, it…
Rank and select queries are basic operations on sequences, with applications in compressed text indexes and other space-efficient data structures. One of the standard data structures supporting these queries is the wavelet tree. In this…
Programming physicists use, as all programmers, arrays, lists, tuples, records, etc., and this requires some change in their thought patterns while converting their formulae into some code, since the "data structures" operated upon, while…