Related papers: Faster Dynamic Compressed d-ary Relations
The rooted tree is an important data structure, and the subtree size, height, and depth are naturally defined attributes of every node. We consider the problem of the existence of a k-ary tree given a list of attribute sequences. We give…
The capability of classifying and clustering a desired set of data is an essential part of building knowledge from data. However, as the size and dimensionality of input data increases, the run-time for such clustering algorithms is…
In this paper, we revisit the problem of indexing multi-dimensional data in memory for the efficient support of multi-dimensional range queries and nearest neighbor queries. This is a classic problem in main-memory databases, where there is…
Any Boolean function corresponds with a complete full binary decision tree. This tree can in turn be represented in a maximally compact form as a direct acyclic graph where common subtrees are factored and shared, keeping only one copy of…
Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on…
The article describes the structural and algorithmic relations between Cartesian trees and Lyndon Trees. This leads to a uniform presentation of the Lyndon table of a word corresponding to the Next Nearest Smaller table of a sequence of…
The k-d tree is a classic binary space-partitioning tree used to organize points in k-dimensional space. While used in computational geometry and graphics, the data structure has a long history of application in nearest neighbor search. The…
The Fenwick tree is a classical implicit data structure that stores an array in such a way that modifying an element, accessing an element, computing a prefix sum and performing a predecessor search on prefix sums all take logarithmic time.…
We show that both the k_T- and collinear factorization for the DIS structure functions can be obtained by consecutive reductions of the Compton scattering amplitude. Each of these reductions is an approximation valid under certain…
We present a new characterization of $k$-trees based on their reduced clique graphs and $(k+1)$-line graphs, which are block graphs. We explore structural properties of these two classes, showing that the number of clique-trees of 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…
This paper examines a common extension of k-medoids and k-median clustering in the case of a two-dimensional Pareto front, as generated by bi-objective optimization approaches. A characterization of optimal clusters is provided, which…
Dynamic programming on tree decompositions is a frequently used approach to solve otherwise intractable problems on instances of small treewidth. In recent work by Bodlaender et al., it was shown that for many connectivity problems, there…
We propose a new outline for adaptive dictionary learning methods for sparse encoding based on a hierarchical clustering of the training data. Through recursive application of a clustering method, the data is organized into a binary…
Zero-suppressed Binary Decision Diagrams (ZDDs) are data structures for representing set families in a compressed form. With ZDDs, many valuable operations on set families can be done in time polynomial in ZDD size. In some cases, however,…
Object Oriented Data Analysis is a new area in statistics that studies populations of general data objects. In this article we consider populations of tree-structured objects as our focus of interest. We develop improved analysis tools for…
A relaxed $k$-ary tree is an ordered directed acyclic graph with a unique source and sink in which every node has out-degree $k$. These objects arise in the compression of trees in which some repeated subtrees are factored and repeated…
In particle simulations, the weights of particles determine how many physical particles they represent. Adaptively adjusting these weights can greatly improve the efficiency of the simulation, without creating severe nonphysical artifacts.…
Visual localization algorithms have achieved significant improvements in performance thanks to recent advances in camera technology and vision-based techniques. However, there remains one critical caveat: all current approaches that are…
This paper introduces a data structure, called simplex tree, to represent abstract simplicial complexes of any dimension. All faces of the simplicial complex are explicitly stored in a trie whose nodes are in bijection with the faces of the…