Related papers: Depth first representations of $k^2$-trees
Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees,…
An optimal binary search tree for an access sequence on elements is a static tree that minimizes the total search cost. Constructing perfectly optimal binary search trees is expensive so the most efficient algorithms construct almost…
We propose a method for linear-time diversity maintenance in particle filtering. It clusters particles based on ancestry tree topology: closely related particles in sufficiently large subtrees are grouped together. The main idea is that the…
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…
Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. $\mathcal{H}^2$-matrices refine this representation following the ideas of fast multipole…
Boundary integral equations lead to dense system matrices when discretized, yet they are data-sparse. Using the $\mathcal{H}$-matrix format, this sparsity is exploited to achieve $\mathcal{O}(N\log N)$ complexity for storage and…
The $k$d-tree is one of the most widely used data structures to manage multi-dimensional data. Due to the ever-growing data volume, it is imperative to consider parallelism in $k$d-trees. However, we observed challenges in existing parallel…
We present several modifications to the previously proposed MSPP algorithm that can speed-up its execution considerably. The MSPP algorithm leverages a multiscale representation of the environment in $n$ dimensions. The information of the…
Establishing the correspondences between newly acquired points and historically accumulated data (i.e., map) through nearest neighbors search is crucial in numerous robotic applications. However, static tree data structures are inadequate…
We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…
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…
Sparse document representations have been widely used to retrieve relevant documents via exact lexical matching. Owing to the pre-computed inverted index, it supports fast ad-hoc search but incurs the vocabulary mismatch problem. Although…
Suffix trees are a fundamental data structure in stringology, but their space usage, though linear, is an important problem for its applications. We design and implement a new compressed suffix tree targeted to highly repetitive texts, such…
Motivation: As a fundamental task in bioinformatics, searching for massive short patterns over a long text is widely accelerated by various compressed full-text indexes. These indexes are able to provide similar searching functionalities to…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
Frequent pattern mining is a relevant method to analyse structured data, like sequences, trees or graphs. It consists in identifying characteristic substructures of a dataset. This paper deals with a new type of patterns for tree data:…
We propose a new succinct representation of labeled trees which represents a tree T using |T|H_k(T) number of bits (plus some smaller order terms), where |T|H_k(T) denotes the k-th order (tree label) entropy, as defined by Ferragina at al.…
The dynamic trees problem is to maintain a forest subject to edge insertions and deletions while facilitating queries such as connectivity, path weights, and subtree weights. Dynamic trees are a fundamental building block of a large number…
The k-truss model is one of the most important models in cohesive subgraph analysis. The k-truss decomposition problem is to compute the trussness of each edge in a given graph, and has been extensively studied. However, the conventional…
Recently, the retrieval models based on dense representations have been gradually applied in the first stage of the document retrieval tasks, showing better performance than traditional sparse vector space models. To obtain high efficiency,…