Related papers: Tree structure compression with RePair

We introduce a new family of compressed data structures to efficiently store and query large string dictionaries in main memory. Our main technique is a combination of hierarchical Front-coding with ideas from longest-common-prefix…

We study low rank approximation of tensors, focusing on the tensor train and Tucker decompositions, as well as approximations with tree tensor networks and more general tensor networks. For tensor train decomposition, we give a bicriteria…

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…

Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is…

Large-alphabet strings are common in scenarios such as information retrieval and natural-language processing. The efficient storage and processing of such strings usually introduces several challenges that are not witnessed in…

The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of…

This paper studies the important problem of finding all $k$-nearest neighbors to points of a query set $Q$ in another reference set $R$ within any metric space. Our previous work defined compressed cover trees and corrected the key…

Machine learning on trees has been mostly focused on trees as input to algorithms. Much less research has investigated trees as output, which has many applications, such as molecule optimization for drug discovery, or hint generation for…

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…

In this paper we present novel algorithmic techniques with a O(H(N)+N/H(N)) time complexity for performing several types of queries and updates on general rooted trees, binary search trees and lists of size N. For rooted trees we introduce…

Ensemble methods are among the state-of-the-art predictive modeling approaches. Applied to modern big data, these methods often require a large number of sub-learners, where the complexity of each learner typically grows with the size of…

In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…

Despite their high accuracy, complex neural networks demand significant computational resources, posing challenges for deployment on resource constrained devices such as mobile phones and embedded systems. Compression algorithms have been…

Given a string $S$ of length $n$, the classic string indexing problem is to preprocess $S$ into a compact data structure that supports efficient subsequent pattern queries. In this paper we consider the basic variant where the pattern is…

We present a novel parsing algorithm for all context-free languages, based on computing the relation between configurations and reaching transitions in a recursive transition network. Parsing complexity w.r.t. input length matches the state…

Much research has been devoted to optimizing algorithms of the Lempel-Ziv (LZ) 77 family, both in terms of speed and memory requirements. Binary search trees and suffix trees (ST) are data structures that have been often used for this…

The kernel method is a potential approach to analyzing structured data such as sequences, trees, and graphs; however, unordered trees have not been investigated extensively. Kimura et al. (2011) proposed a kernel function for unordered…

Given a set of pattern strings $\mathcal{P}=\{P_1, P_2,\ldots P_k\}$ and a text string $S$, the classic dictionary matching problem is to report all occurrences of each pattern in $S$. We study the dictionary problem in the compressed…

In tree based adaptive mesh refinement, elements are partitioned between processes using a space filling curve. The curve establishes an ordering between all elements that derive from the same root element, the tree. When representing more…

Constrained counting is a fundamental problem in artificial intelligence. A promising new algebraic approach to constrained counting makes use of tensor networks, following a reduction from constrained counting to the problem of…