Related papers: An algorithm for generating random mixed-arity tre…
In this paper, we introduce a new representation for ordered trees, the weight sequence representation. We then use this to construct new representations for both rooted trees and free trees, namely the canonical weight sequence…
The properties of randomly evolving special trees having defined and analyzed already in two earlier papers (arXiv:cond-mat/0205650 and arXiv:cond-mat/0211092) have been investigated in the case when the continuous time parameter converges…
Several structure-learning algorithms for staged trees, asymmetric extensions of Bayesian networks, have been proposed. However, these either do not scale efficiently as the number of variables considered increases, a priori restrict the…
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…
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…
Unbiased random vectors i.e. distributed uniformly in n-dimensional space, are widely applied and the computational cost of generating a vector increases only linearly with n. On the other hand, generating uniformly distributed random…
We present a randomized algorithm for reconstructing directed rooted trees of $n$ nodes and node degree at most $d$, by asking at most $O(dn\log^2 n)$ path queries. Each path query takes as input an origin node and a target node, and…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
A fringe subtree of a rooted tree is a subtree induced by one of the vertices and all its descendants. We consider the problem of estimating the number of distinct fringe subtrees in two types of random trees: simply generated trees and…
The potential lack of fairness in the outputs of machine learning algorithms has recently gained attention both within the research community as well as in society more broadly. Surprisingly, there is no prior work developing tree-induction…
A graph generative model defines a distribution over graphs. One type of generative model is constructed by autoregressive neural networks, which sequentially add nodes and edges to generate a graph. However, the likelihood of a graph under…
Motivated by the study of pattern avoidance in the context of permutations and ordered partitions, we consider the enumeration of weak-ordering chains obtained as leaves of certain restricted rooted trees. A tree of order $n$ is generated…
This paper presents a new kind of self-balancing ternary search trie that uses a randomized balancing strategy adapted from Aragon and Seidel's randomized binary search trees ("treaps"). After any sequence of insertions and deletions of…
We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactification; it also gives a representation of the limit in…
We introduce an exact distributed algorithm to train Random Forest models as well as other decision forest models without relying on approximating best split search. We explain the proposed algorithm and compare it to related approaches for…
We study the influence of the seed in random trees grown according to the uniform attachment model, also known as uniform random recursive trees. We show that different seeds lead to different distributions of limiting trees from a total…
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…
A widely used method for determining the similarity of two labeled trees is to compute a maximum agreement subtree of the two trees. Previous work on this similarity measure is only concerned with the comparison of labeled trees of two…
The Rabin tree theorem yields an algorithm to solve the satisfiability problem for monadic second-order logic over infinite trees. Here we solve the probabilistic variant of this problem. Namely, we show how to compute the probability that…