Related papers: LRM-Trees: Compressed Indices, Adaptive Sorting, a…
Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely one cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect…
Wavelet trees are widely used in the representation of sequences, permutations, text collections, binary relations, discrete points, and other succinct data structures. We show, however, that this still falls short of exploiting all of the…
Previous compact representations of permutations have focused on adding a small index on top of the plain data $<\pi(1), \pi(2),...\pi(n)>$, in order to efficiently support the application of the inverse or the iterated permutation. In this…
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…
The Block Tree (BT) is a novel compact data structure designed to compress sequence collections. It obtains compression ratios close to Lempel-Ziv and supports efficient direct access to any substring. The BT divides the text recursively…
Efficient methods for storing and querying are critical for scaling high-order n-gram language models to large corpora. We propose a language model based on compressed suffix trees, a representation that is highly compact and can be easily…
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…
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…
Suffix trees are one of the most versatile data structures in stringology, with many applications in bioinformatics. Their main drawback is their size, which can be tens of times larger than the input sequence. Much effort has been put into…
Given a string $S$ of $n$ integers in $[0,\sigma)$, a range minimum query RMQ$(i, j)$ asks for the index of the smallest integer in $S[i \dots j]$. It is well known that the problem can be solved with a succinct data structure of size $2n +…
This paper contains a classification of countable lower 1-transitive linear orders. The notion of lower 1-transitivity generalises that of 1-transitivity for linear orders, and is essential for the structure theory of 1-transitive trees.…
We study the compressed representation of a ranked tree by a (string) straight-line program (SLP) for its preorder traversal, and compare it with the well-studied representation by straight-line context free tree grammars (which are also…
Log-Structured Merge (LSM) Trees provide a tiered data storage and retrieval paradigm that is attractive for write-optimized data systems. Maintaining an efficient buffer in memory and deferring updates past their initial write-time, the…
The quadratic complexity of self-attention constrains Large Language Models (LLMs) in processing long contexts, a capability essential for many advanced applications. Context compression aims to alleviate this computational bottleneck while…
We propose an extension of tree-based space-partitioning indexing structures for data with low intrinsic dimensionality embedded in a high dimensional space. We call this extension an Angle Tree. Our extension can be applied to both…
Tree methods (recursive partitioning) are a popular class of nonparametric methods for analyzing data. One extension of the basic tree methodology is the survival tree, which applies recursive partitioning to censored survival data. There…
Trees are fundamental data structure for many areas of computer science and system engineering. In this report, we show how to ensure eventual consistency of optimistically replicated trees. In optimistic replication, the different replicas…
Efficient spatial indexing is crucial for processing large-scale spatial data. Traditional spatial indexes, such as STR-Tree and Quad-Tree, organize spatial objects based on coarse approximations, such as their minimum bounding rectangles…
Tree ensembles are very popular machine learning models, known for their effectiveness in supervised classification and regression tasks. Their performance derives from aggregating predictions of multiple decision trees, which are renowned…
We study the design of efficient algorithms for combinatorial pattern matching. More concretely, we study algorithms for tree matching, string matching, and string matching in compressed texts.