Related papers: On Succinct Representations of Binary Trees
Let $n$ denote the number of elements currently in a data structure. An in-place heap is stored in the first $n$ locations of an array, uses $O(1)$ extra space, and supports the operations: minimum, insert, and extract-min. We introduce an…
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…
Sorting is a foundational problem in computer science that is typically employed on sequences or total orders. More recently, a more general form of sorting on partially ordered sets (or posets), where some pairs of elements are…
We consider the problem of compactly representing the Depth First Search (DFS) tree of a given undirected or directed graph having $n$ vertices and $m$ edges while supporting various DFS related queries efficiently in the RAM with…
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…
We consider a construction of the fundamental spin representations of the simple Lie algebras $\mathfrak{so}(n)$ in terms of binary arithmetic of fixed width integers. This gives the spin matrices as a Lie subalgebra of a…
We present a bijection between some quadrangular dissections of an hexagon and unrooted binary trees, with interesting consequences for enumeration, mesh compression and graph sampling. Our bijection yields an efficient uniform random…
We present linear-space data structures for several frequency queries on trees, namely: path mode, path least frequent element, and path $\alpha$-minority queries. We present the first linear-space data structures, requiring $O(n…
There is a common problem of operating on hash values of elements of some database. In this paper there will be analyzed informational content of such general task and how to practically approach such found lower boundaries. Minimal prefix…
We consider compact representations of collections of similar strings that support random access queries. The collection of strings is given by a rooted tree where edges are labeled by an edit operation (inserting, deleting, or replacing a…
The longest common prefix (LCP) array is a versatile auxiliary data structure in indexed string matching. It can be used to speed up searching using the suffix array (SA) and provides an implicit representation of the topology of an…
Phylogenetic (evolutionary) trees and networks are leaf-labeled graphs that are widely used to represent the evolutionary relationships between entities such as species, languages, cancer cells, and viruses. To reconstruct and analyze…
We describe a data structure that supports access, rank and select queries, as well as symbol insertions and deletions, on a string $S[1,n]$ over alphabet $[1..\sigma]$ in time $O(\lg n/\lg\lg n)$, which is optimal even on binary sequences…
We study leaf-to-ancestor path-minimum queries on a rooted, weighted tree in the oracle model, where the only allowed value operation is a comparison oracle on edge (or node) weights. We give a static data structure that, after O(n log h)…
We prove that given a discrete space with $n$ points which is either embedded in a system of $k$ trees, or the Cartesian product of $k$ trees, we can compute all eccentricities in ${\cal O}(2^{{\cal O}(k\log{k})}(N+n)^{1+o(1)})$ time, where…
Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. This variant requires merging two paths in a single operation. In contrast to the standard…
We present a linear time algorithm for computing an implicit linear space representation of a minimum cycle basis (MCB) in weighted partial 2-trees, i.e., graphs of treewidth two. The implicit representation can be made explicit in a…
Good representations for phylogenetic trees and networks are important for optimizing storage efficiency and implementation of scalable methods for the inference and analysis of evolutionary trees for genes, genomes and species. We…
The decision tree is one of the most fundamental programming abstractions. A commonly used type of decision tree is the alphabetic binary tree, which uses (without loss of generality) ``less than'' versus ''greater than or equal to'' tests…
Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of…