Related papers: Traversing Grammar-Compressed Trees with Constant …
Contention tree algorithm is initially invented as a solution to improve the stable throughput problem of Slotted ALOHA in multiple access schemes. Even though the throughput is stabilized in tree algorithms, the delay of requests may grow…
In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…
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…
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…
In terms of signal samples, we propose and justify a new rank reduced multi-term transform, abbreviated as MTT, which, under certain conditions, may provide better-associated accuracy than that of known optimal rank reduced transforms. The…
String diagrams are a powerful tool for reasoning about composite structures in symmetric monoidal categories. By representing string diagrams as graphs, equational reasoning can be done automatically by double-pushout rewriting. !-graphs…
Language exhibits structure at different scales, ranging from subwords to words, sentences, paragraphs, and documents. To what extent do deep models capture information at these scales, and can we force them to better capture structure…
Offering rich contexts to Large Language Models (LLMs) has shown to boost the performance in various tasks, but the resulting longer prompt would increase the computational cost and might exceed the input limit of LLMs. Recently, some…
The most fundamental problem considered in algorithms for text processing is pattern matching: given a pattern $p$ of length $m$ and a text $t$ of length $n$, does $p$ occur in $t$? Multiple versions of this basic question have been…
Legged robots are popular candidates for missions in challenging terrains due to the wide variety of locomotion strategies they can employ. Terrain classification is a key enabling technology for autonomous legged robots, as it allows the…
Practical data structures for the edit-sensitive parsing (ESP) are proposed. Given a string S, its ESP tree is equivalent to a context-free grammar G generating just S, which is represented by a DAG. Using the succinct data structures for…
Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics (the study of evolutionary trees and networks). Although these networks have a number of attractive mathematical…
Tensors are often studied by introducing preorders such as restriction and degeneration: the former describes transformations of the tensors by local linear maps on its tensor factors; the latter describes transformations where the local…
In biology, a phylogenetic tree is a tool to represent the evolutionary relationship between species. Unfortunately, the classical Schr\"oder tree model is not adapted to take into account the chronology between the branching nodes. In…
A staged tree model is a discrete statistical model encoding relationships between events. These models are realised by directed trees with coloured vertices. In algebro-geometric terms, the model consists of points inside a toric variety.…
Phylogenetic tree shapes capture fundamental signatures of evolution. We consider ``ranked'' tree shapes, which are equipped with a total order on the internal nodes compatible with the tree graph. Recent work has established an elegant…
Exposing latent knowledge in geospatial trajectories has the potential to provide a better understanding of the movements of individuals and groups. Motivated by such a desire, this work presents the context tree, a new hierarchical data…
We present an algorithm for searching regular expression matches in compressed text. The algorithm reports the number of matching lines in the uncompressed text in time linear in the size of its compressed version. We define efficient data…
Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward…
We present a new algorithm for subsequence matching in grammar compressed strings. Given a grammar of size $n$ compressing a string of size $N$ and a pattern string of size $m$ over an alphabet of size $\sigma$, our algorithm uses…