Related papers: Cartesian trees and Lyndon trees

A phylogenetic tree shows the evolutionary relationships among species. Internal nodes of the tree represent speciation events and leaf nodes correspond to species. A goal of phylogenetics is to combine such trees into larger trees, called…

Rectangular layouts, subdivisions of an outer rectangle into smaller rectangles, have many applications in visualizing spatial information, for instance in rectangular cartograms in which the rectangles represent geographic or political…

We introduce and study the {\em orderly spanning trees} of plane graphs. This algorithmic tool generalizes {\em canonical orderings}, which exist only for triconnected plane graphs. Although not every plane graph admits an orderly spanning…

Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…

Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…

We introduce the zip tree, a form of randomized binary search tree that integrates previous ideas into one practical, performant, and pleasant-to-implement package. A zip tree is a binary search tree in which each node has a numeric rank…

\begin{abstract} Greedy permutations, also known as Gonzalez Orderings or Farthest Point Traversals are a standard way to approximate $k$-center clustering and have many applications in sampling and approximating metric spaces. A greedy…

Based on Lyndon words, a new Sudoku-like puzzle is presented and some relative theoretical questions are proposed.

The classical matrix-tree theorem relates the determinant of the combinatorial Laplacian on a graph to the number of spanning trees. We generalize this result to Laplacians on one- and two-dimensional vector bundles, giving a combinatorial…

Tree decompositions were developed by Robertson and Seymour. Since then algorithms have been developed to solve intractable problems efficiently for graphs of bounded treewidth. In this paper we extend tree decompositions to allow cycles 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…

We define a mapping from transition-based parsing algorithms that read sentences from left to right to sequence labeling encodings of syntactic trees. This not only establishes a theoretical relation between transition-based parsing and…

We explore a physical model of ordered sums of integers as trains of rods. The trains for a fixed, possibly infinite, set of rod lengths naturally correspond to nodes in a tree; relations among finite linear recursions encoded in the…

With the development of connected filters for the last decade, many algorithms have been proposed to compute the max-tree. Max-tree allows to compute the most advanced connected operators in a simple way. However, no fair comparison of…

A consensus tree is a phylogenetic tree that captures the similarity between a set of conflicting phylogenetic trees. The problem of computing a consensus tree is a major step in phylogenetic tree reconstruction. It also finds applications…

Tree kernels are fundamental tools that have been leveraged in many applications, particularly those based on machine learning for Natural Language Processing tasks. In this paper, we devise a parallel implementation of the sequential…

A heuristic extending the Squarified Treemap technique for the representation of hierarchical information as treemaps is presented. The original technique gives high quality treemap views, since items are laid out with rectangles that…

A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…

Using (a,b)-trees as an example, we show how to perform a parallel split with logarithmic latency and parallel join, bulk updates, intersection, union (or merge), and (symmetric) set difference with logarithmic latency and with information…

The rank (also known as protection number or leaf-height) of a vertex in a rooted tree is the minimum distance between the vertex and any of its leaf descendants. We consider the sum of ranks over all vertices (known as the security) in…