Related papers: Faster Dynamic Compressed d-ary Relations
We consider $k$-dimensional discrete-time systems of the form $x_{n+1}=F(x_n,\ldots,x_{n-k+1})$ in which the map $F$ is continuous and monotonic in each one of its arguments. We define a partial order on $\mathbb{R}^{2k}_+$, compatible with…
The successor and predecessor problem consists of obtaining the closest value in a set of integers, greater/smaller than a given value. This problem has interesting applications, like the intersection of inverted lists. It can be easily…
Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of…
We present an empirical analysis of data structures for approximate nearest neighbor searching. We compare the well-known optimized kd-tree splitting method against two alternative splitting methods. The first, called the sliding-midpoint…
This paper proposes FREEtree, a tree-based method for high dimensional longitudinal data with correlated features. Popular machine learning approaches, like Random Forests, commonly used for variable selection do not perform well when there…
The task of computing homomorphisms between two finite relational structures $\mathcal{A}$ and $\mathcal{B}$ is a well-studied question with numerous applications. Since the set $\operatorname{Hom}(\mathcal{A},\mathcal{B})$ of all…
Implicit Neural Representations for Videos (NeRV) have emerged as a powerful paradigm for video representation, enabling direct mappings from frame indices to video frames. However, existing NeRV-based methods do not fully exploit temporal…
We study compact straight-line embeddings of trees. We show that perfect binary trees can be embedded optimally: a tree with $n$ nodes can be drawn on a $\sqrt n$ by $\sqrt n$ grid. We also show that testing whether a given binary tree has…
A dynamic forest data structure maintains a forest (and associated data like edge weights) under edge insertions and deletions. Dynamic forests are widely used to solve online and offline graph problems. Well-known examples of dynamic…
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…
The problem of storing a set of strings --- a string dictionary --- in compact form appears naturally in many cases. While classically it has represented a small part of the whole data to be processed (e.g., for Natural Language processing…
Representations of Spin groups and Clifford algebras derived from the structure of qubit trees are introduced in this work. For ternary trees the construction is more general and reduction to binary trees is formally defined by deletion of…
We discuss the foundations of 2-dimensional graphical languages, with a view towards their computer implementation in a 'compiler' for monoidal categories. In particular, we discuss the close relationship between string diagrams, pasting…
This paper is concerned with the approximation of high-dimensional functions in a statistical learning setting, by empirical risk minimization over model classes of functions in tree-based tensor format. These are particular classes of…
Minimum spanning trees (MSTs) provide a convenient representation of datasets in numerous pattern recognition activities. Moreover, they are relatively fast to compute. In this paper, we quantify the extent to which they are meaningful in…
Projected Hartree-Fock theory provides an accurate description of many kinds of strong correlations but does not properly describe weakly-correlated systems. On the other hand, single-reference methods such as configuration interaction or…
Now a days many algorithms are invented or being inventing to find the solution for Euclidean Minimum Spanning Tree, EMST, problem, as its applicability is increasing in much wide range of fields containing spatial or spatio temporal data…
Answering connectivity queries is fundamental to fully dynamic graphs where edges and vertices are inserted and deleted frequently. Existing work proposes data structures and algorithms with worst-case guarantees. We propose a new data…
In this paper we investigate the use of the concept of tree dimension in Horn clause analysis and verification. The dimension of a tree is a measure of its non-linearity - for example a list of any length has dimension zero while a complete…
Hypertree decompositions of hypergraphs are a generalization of tree decompositions of graphs. The corresponding hypertree-width is a measure for the cyclicity and therefore tractability of the encoded computation problem. Many NP-hard…