相关论文: An Extended Symbolic-Arithmetic Model for Teaching…

A red-black (RB) tree is a data structure with red and black nodes coloration. The red and black color of nodes make up the principal component for balancing a RB tree. A balanced tree has an equal number of black nodes on any simple path.…

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…

A bilateralist take on proof-theoretic semantics can be understood as demanding of a proof system to display not only rules giving the connectives' provability conditions but also their refutability conditions. On such a view, then, a…

We study a method of reducing space dimension in multi-dimensional Black-Scholes partial differential equations as well as in multi-dimensional parabolic equations. We prove that a multiplicative transformation of space variables in 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,…

[RETRACTED]Data increasingly abounds, but distilling their underlying relationships down to something interpretable remains challenging. One approach is genetic programming, which `symbolically regresses' a data set down into an equation.…

A new approach to solving a class of rankconstrained semi-definite programming (SDP) problems, which appear in many signal processing applications such as transmit beamspace design in multiple-input multiple-output (MIMO) radar, downlink…

In this paper, we introduce a modified version of the renormalization group (RG) method and test its numerical accuracy. It has been tested on numerous scalar ODEs and systems of ODEs. Our method is primarily motivated by the possibility of…

Reciprocal best match graphs (RBMGs) are vertex colored graphs whose vertices represent genes and the colors the species where the genes reside. Edges identify pairs of genes that are most closely related with respect to an underlying…

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…

We revisit two well-studied problems, Bounded Degree Vertex Deletion and Defective Coloring, where the input is a graph $G$ and a target degree $\Delta$ and we are asked either to edit or partition the graph so that the maximum degree…

We study restricted computation models related to the Tree Evaluation Problem}. The TEP was introduced in earlier work as a simple candidate for the (*very*) long term goal of separating L and LogDCFL. The input to the problem is a rooted,…

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…

Accurately modelling the dynamics of complex systems and discovering their governing differential equations are critical tasks for accelerating scientific discovery. Using noisy, synthetic data from two damped oscillatory systems, we…

Node elimination is a numerical approach to obtain cubature rules for the approximation of multivariate integrals. Beginning with a known cubature rule, nodes are selected for elimination, and a new, more efficient rule is constructed by…

Balliu et al. (DISC 2020) classified the hardness of solving binary labeling problems with distributed graph algorithms; in these problems the task is to select a subset of edges in a $2$-colored tree in which white nodes of degree $d$ and…

We prove several new tight distributed lower bounds for classic symmetry breaking graph problems. As a basic tool, we first provide a new insightful proof that any deterministic distributed algorithm that computes a $\Delta$-coloring on…

In the past few years, a successful line of research has lead to lower bounds for several fundamental local graph problems in the distributed setting. These results were obtained via a technique called round elimination. On a high level,…