Related papers: Randomized Ternary Search Tries
We introduce a model for the retrieval of information hidden in legal texts. These are typically organised in a hierarchical (tree) structure, which a reader interested in a given provision needs to explore down to the "deepest" level…
Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…
Consider the following generalization of the classic binary search problem: a searcher is required to find a hidden vertex $x$ in a tree $T$. To do so, they iteratively perform queries to an oracle, each about a chosen vertex $v$. After…
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…
We give an algorithm to enumerate the results on trees of monadic second-order (MSO) queries represented by nondeterministic tree automata. After linear time preprocessing (in the input tree), we can enumerate answers with linear delay (in…
Given a set S of n \geq d points in general position in R^d, a random hyperplane split is obtained by sampling d points uniformly at random without replacement from S and splitting based on their affine hull. A random hyperplane search tree…
Searching in partially ordered structures has been considered in the context of information retrieval and efficient tree-like indexes, as well as in hierarchy based knowledge representation. In this paper we focus on tree-like partial…
Frequent tree mining asks us to enumerate tree patterns that occur frequently in a database of rooted trees. This problem is motivated by tree-structured data in bioinformatics, such as glycans and pseudoknot-free RNA secondary structures.…
Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…
Algorithms for efficiently finding optimal alphabetic decision trees -- such as the Hu-Tucker algorithm -- are well established and commonly used. However, such algorithms generally assume that the cost per decision is uniform and thus…
While modern biotechnologies allow synthesizing new proteins and function measurements at scale, efficiently exploring a protein sequence space and engineering it remains a daunting task due to the vast sequence space of any given protein.…
In this article, we calculate the mean throughput, number of collisions, successes, and idle slots for random tree algorithms with successive interference cancellation. Except for the case of the throughput for the binary tree, all the…
This paper introduces a series of methods for traversing binary decision trees using arithmetic operations. We present a suite of binary tree traversal algorithms that leverage novel representation matrices to flatten the full binary tree…
When combined properly, search techniques can reveal the full potential of sophisticated branching heuristics. We demonstrate this observation on the well-known class of random 3-SAT formulae. First, a new branching heuristic is presented,…
It is widely assumed that $O(m+\lg \sigma)$ is the best one can do for finding a pattern of length $m$ in a compacted trie storing strings over an alphabet of size $\sigma$, if one insists on linear-size data structures and deterministic…
This report investigates three fundamental search algorithms: Linear Search, Binary Search, and Two Pointer Search. Linear Search checks each element sequentially, Binary Search divides the search space in half, and Two Pointer Search uses…
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…
Space partitioning methods such as random forests and the Mondrian process are powerful machine learning methods for multi-dimensional and relational data, and are based on recursively cutting a domain. The flexibility of these methods is…
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…
In this paper, we provide a polynomial time algorithm to calculate the probability of a {\it ranked} gene tree topology for a given species tree, where a ranked tree topology is a tree topology with the internal vertices being ordered. The…