相关论文: A symbolic-arithmetic for teaching double-black no…

Double-black (DB) nodes have no place in red-black (RB) trees. So when DB nodes are formed, they are immediately removed. The removal of DB nodes that cause rotation and recoloring of other connected nodes poses greater challenges in the…

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…

The original description of the k-d tree recognized that rebalancing techniques, used for building an AVL or red-black tree, are not applicable to a k-d tree, because these techniques involve cyclic exchange of tree nodes that violates the…

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 $n$…

We show how a few modifications to the red-black trees allow for $O(1)$ worst-case update time (once the position of the inserted or deleted element is known). The resulting structure is based on relaxing some of the properties of the…

We study a tree coloring model introduced by Guidon (2018), initially based on an analogy with a remote control system of a rail yard, seen as switches on a binary tree. For a given binary tree, we formalize the constraints on the coloring,…

The entities in directed networks arising from real-world interactions are often naturally organized under some hierarchical structure. Given a directed, weighted, graph with edges and node labels, we introduce ranking problem where the…

Distributed databases often suffer unequal distribution of data among storage nodes, which is known as `data skew'. Data skew arises from a number of causes such as removal of existing storage nodes and addition of new empty nodes to the…

Multi-task learning aims to learn multiple related tasks simultaneously and has achieved great success in various fields. However, the disparity in loss and gradient scales among tasks often leads to performance compromises, and the…

This paper describes the most efficient way to manage operations on ranges of elements within an ordered set. The goal is to improve existing solutions, by optimizing the average-case time complexity and getting rid of heavy multiplicative…

Fair graph partition of social networks is a crucial step toward ensuring fair and non-discriminatory treatments in unsupervised user analysis. Current fair partition methods typically consider node balance, a notion pursuing a…

The paper presents a technique for constructing noisy data structures called a walking tree. We apply it for a Red-Black tree (an implementation of a Self-Balanced Binary Search Tree) and a segment tree. We obtain the same complexity of the…

This paper proposes a new method for interpreting and simplifying a black box model of a deep random forest (RF) using a proposed rule elimination. In deep RF, a large number of decision trees are connected to multiple layers, thereby…

When choosing a suitable technique for regression and classification with multivariate predictor variables, one is often faced with a tradeoff between interpretability and high predictive accuracy. To give a classical example,…

Deep Neural Networks (DNNs) are ubiquitous in today's computer vision land-scape, despite involving considerable computational costs. The mainstream approaches for runtime acceleration consist in pruning connections (unstructured pruning)…

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…

Large tree structures are ubiquitous and real-world relational datasets often have information associated with nodes (e.g., labels or other attributes) and edges (e.g., weights or distances) that need to be communicated to the viewers. Yet,…

This study introduces a new method of visualizing complex tree structured objects. The usefulness of this method is illustrated in the context of detecting unexpected features in a data set of very large trees. The major contribution is a…

This article compares the performance of the AVL tree to the performance of the bottom-up, top-down, and left-leaning red-black trees. The bottom-up red-black tree is faster than the AVL tree for insertion and deletion of randomly ordered…

Node classification is an important task to solve in graph-based learning. Even though a lot of work has been done in this field, imbalance is neglected. Real-world data is not perfect, and is imbalanced in representations most of the…