Related papers: Using rational numbers to key nested sets

Many innovations are inspired by past ideas in a non-trivial way. Tracing these origins and identifying scientific branches is crucial for research inspirations. In this paper, we use citation relations to identify the descendant chart,…

We consider here the problem of chaining seeds in ordered trees. Seeds are mappings between two trees Q and T and a chain is a subset of non overlapping seeds that is consistent with respect to postfix order and ancestrality. This problem…

For a pair consisting of a gene tree and a species tree, the ancestral configurations at an internal node of the species tree are the distinct sets of gene lineages that can be present at that node. Ancestral configurations appear in…

LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to…

Many common sequential data sources, such as source code and natural language, have a natural tree-structured representation. These trees can be generated by fitting a sequence to a grammar, yielding a hierarchical ordering of the tokens in…

We study the enumeration of spinal tree-child phylogenetic networks, a rigid family of tree-child networks in which all internal vertices lie on a single root--to--leaf path. We provide two complementary combinatorial frameworks. First, we…

In this paper, we introduce TreeCoders, a novel family of transformer trees. We moved away from traditional linear transformers to complete k-ary trees. Transformer blocks serve as nodes, and generic classifiers learn to select the best…

Farey sequences, Stern-Brocot sequences, the Calkin-Wilf sequences are shown to be generated via almost identical second order recurrence relations. These sequences have combinatorial, computational, and geometric applications, and are…

The output structure of database-like tables, consisting of values structured in horizontal rows and vertical columns identifiable by name, can cover a wide range of NLP tasks. Following this constatation, we propose a framework for…

In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms. The…

We present a method for constructing taxonomic trees (e.g., WordNet) using pretrained language models. Our approach is composed of two modules, one that predicts parenthood relations and another that reconciles those predictions into trees.…

Generating texts from structured data (e.g., a table) is important for various natural language processing tasks such as question answering and dialog systems. In recent studies, researchers use neural language models and encoder-decoder…

We apply distributed language embedding methods from Natural Language Processing to assign a vector to each database entity associated token (for example, a token may be a word occurring in a table row, or the name of a column). These…

We use reinforcement learning to learn tree-structured neural networks for computing representations of natural language sentences. In contrast with prior work on tree-structured models in which the trees are either provided as input or…

Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population \cite{nature_01}. This result brings our attention again to a math problem related to inbreeding family trees…

We describe a novel classifier with a tree structure, designed using information theory concepts. This Information Network is made of information nodes, that compress the input data, and multiplexers, that connect two or more input nodes to…

In this paper, we consider the problem of distributed inference in tree based networks. In the framework considered in this paper, distributed nodes make a 1-bit local decision regarding a phenomenon before sending it to the fusion center…

We investigate the distribution of the depth of a node containing a specific key or, equivalently, the number of steps needed to retrieve an item stored in a randomly grown binary search tree. Using a representation in terms of mixed and…

We study leaf-to-ancestor path-minimum queries on a rooted, weighted tree in the oracle model, where the only allowed value operation is a comparison oracle on edge (or node) weights. We give a static data structure that, after O(n log h)…

Provenance for database queries or scientific workflows is often motivated as providing explanation, increasing understanding of the underlying data sources and processes used to compute the query, and reproducibility, the capability to…