Related papers: Analysis of d-ary Tree Algorithms with Successive …
This paper considers the enumeration of trees avoiding a contiguous pattern. We provide an algorithm for computing the generating function that counts n-leaf binary trees avoiding a given binary tree pattern t. Equipped with this counting…
We advance the recently proposed neuro-symbolic Differentiable Tree Machine, which learns tree operations using a combination of transformers and Tensor Product Representations. We investigate the architecture and propose two key…
Tree data structures, such as red-black trees, quad trees, treaps, or tries, are fundamental tools in computer science. A classical problem in concurrency is to obtain expressive, efficient, and scalable versions of practical tree data…
Work introduces a hierarchical binary tree-based reduction that replaces standard self-attention. The core idea is to use a recursive Gated Linear Unit merge operation, achieving O(n) total merge operations O(log n) parallel depth O(n d^2)…
We comment on old and new results related to the destruction of a random recursive tree (RRT), in which its edges are cut one after the other in a uniform random order. In particular, we study the number of steps needed to isolate or…
Rebalancing schemes for dynamic binary search trees are numerous in the literature, where the goal is to maintain trees of low height, either in the worst-case or expected sense. In this paper we study randomized rebalancing schemes for…
In this study we explore the performance gain that can be achieved at the network level by employing successive interference cancelation (SIC) instead of treating interference as noise for random access wireless mesh networks with…
This paper provides a unified framework to study the performance of successive interference cancellation (SIC) in wireless networks with arbitrary fading distribution and power-law path loss. An analytical characterization of the…
We discuss a notion of convergence for binary trees that is based on subtree sizes. In analogy to recent developments in the theory of graphs, posets and permutations we investigate some general aspects of the topology, such as a…
At present, operators address the explosive growth of mobile data demand by densification of the cellular network so as to reduce the transmitter-receiver distance and to achieve higher spectral efficiency. Due to such network densification…
This paper introduces the Trinary decision tree, an algorithm designed to improve the handling of missing data in decision tree regressors and classifiers. Unlike other approaches, the Trinary decision tree does not assume that missing…
We examine a discrete random recursive tree growth process that, at each time step, either adds or deletes a node from the tree with probability $p$ and $1-p$, respectively. Node addition follows the usual uniform attachment model. For node…
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 study the random m-ary search tree model (where m stands for the number of branches of a search tree), an important problem for data storage in computer science, using a variety of statistical physics techniques that allow us to obtain…
Imitating a recently introduced invariant of trees, we initiate the study of the inducibility of $d$-ary trees (rooted trees whose vertex outdegrees are bounded from above by $d\geq 2$) with a given number of leaves. We determine the exact…
In this paper, we provide algorithms to rank, unrank, and randomly generate certain degree-restricted classes of Cayley trees. Specifically, we consider classes of trees that have a given degree sequence or a given multiset of degrees. If…
This paper presents the first implementation of a search tree data structure in an asynchronous shared-memory system that provides a wait-free algorithm for executing range queries on the tree, in addition to non-blocking algorithms for…
Balanced search trees are widely used in computer science to efficiently maintain dynamic ordered data. To support efficient set operations (e.g., union, intersection, difference) using trees, the join-based framework is widely studied.…
Inspired by [4] we present a new algorithm for uniformly random generation of ordered trees in which all occuring outdegrees can be specified by a given sequence of numbers. The method can be used for random generation of binary or n-ary…
Nowadays, multiprocessing is mainstream with exponentially increasing number of processors. Load balancing is, therefore, a critical operation for the efficient execution of parallel algorithms. In this paper we consider the fundamental…