Related papers: A Dynamic, Self-balancing k-d Tree
We present a dynamic self-balancing octree data structure that enables efficient neighborhood maintenance in evolving metric spaces, a key challenge in modern machine learning systems. Many learning and generative models operate as…
We consider replication-based distributed storage systems in which each node stores the same quantum of data and each data bit stored has the same replication factor across the nodes. Such systems are referred to as balanced distributed…
Different spatial objects that vary in their characteristics, such as molecular biology and geography, are presented in spatial areas. Methods to organize, manage, and maintain those objects in a structured manner are required. Data mining…
Net-trees are a general purpose data structure for metric data that have been used to solve a wide range of algorithmic problems. We give a simple randomized algorithm to construct net-trees on doubling metrics using $O(n\log n)$ time in…
We present a novel distributed union-find algorithm that features asynchronous parallelism and k-d tree based load balancing for scalable visualization and analysis of scientific data. Applications of union-find include level set extraction…
The tree is an essential data structure in many applications. In a distributed application, such as a distributed file system, the tree is replicated.To improve performance and availability, different clients should be able to update their…
Galled trees, directed acyclic graphs that model evolutionary histories with isolated hybridization events, have become very popular due to both their biological significance and the existence of polynomial time algorithms for their…
The supertree problem asking for a tree displaying a set of consistent input trees has been largely considered for the reconstruction of species trees. Here, we rather explore this framework for the sake of reconstructing a gene tree from a…
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…
Flat combining is a concurrency threaded technique whereby one thread performs all the operations in batch by scanning a queue of operations to-be-done and performing them together. Flat combining makes sense as long as k operations each…
Tree trace reconstruction aims to learn the binary node labels of a tree, given independent samples of the tree passed through an appropriately defined deletion channel. In recent work, Davies, R\'acz, and Rashtchian used combinatorial…
In this paper, multivalued data or multiple values variables are defined. They are typical when there is some intrinsic uncertainty in data production, as the result of imprecise measuring instruments, such as in image recognition, in human…
Dynamic tree data structures maintain a forest while supporting insertion and deletion of edges and a broad set of queries in $O(\log n)$ time per operation. Such data structures are at the core of many modern algorithms. Recent work has…
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…
We tackle the challenging problem of creating full and accurate three dimensional reconstructions of botanical trees with the topological and geometric accuracy required for subsequent physical simulation, e.g. in response to wind forces.…
We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function based on a novel formulation of the constrained problem. Then…
Frequencies of $k$-mers in sequences are sometimes used as a basis for inferring phylogenetic trees without first obtaining a multiple sequence alignment. We show that a standard approach of using the squared-Euclidean distance between…
In a reconfiguration problem, given a problem and two feasible solutions of the problem, the task is to find a sequence of transformations to reach from one solution to the other such that every intermediate state is also a feasible…
Red-black (RB) trees are one of the most efficient variants of balanced binary search trees. However, they have always been blamed for being too complicated, hard to explain, and not suitable for pedagogical purposes. In the pioneering work…
In this paper, we are interested in the number of red nodes in red-black trees. We first present an $O(n^2\log n)$ time dynamic programming solution for computing $r(n)$, the largest number of red internal nodes in a red-black tree on $n$…