Related papers: Work-efficient Batch-incremental Minimum Spanning …
In the minimum $k$-edge-connected spanning subgraph ($k$-ECSS) problem the goal is to find the minimum weight subgraph resistant to up to $k-1$ edge failures. This is a central problem in network design, and a natural generalization of the…
A singularly (near) optimal distributed algorithm is one that is (near) optimal in \emph{two} criteria, namely, its time and message complexities. For \emph{synchronous} CONGEST networks, such algorithms are known for fundamental…
Finding the minimum spanning tree (MST) of a graph is an important task in computer vision, as it enables a sparse and low-cost representation of connectivity among elements (such as superpixels, points, or regions), which is useful for…
Dimensionality reduction is a crucial first step for many unsupervised learning tasks including anomaly detection and clustering. Autoencoder is a popular mechanism to accomplish dimensionality reduction. In order to make dimensionality…
Maintaining a $k$-core decomposition quickly in a dynamic graph has important applications in network analysis. The main challenge for designing efficient exact algorithms is that a single update to the graph can cause significant global…
We consider a special case of the generalized minimum spanning tree problem (GMST) and the generalized travelling salesman problem (GTSP) where we are given a set of points inside the integer grid (in Euclidean plane) where each grid cell…
We present a set of parallel algorithms for computing exact k-nearest neighbors in low dimensions. Many k-nearest neighbor algorithms use either a kd-tree or the Morton ordering of the point set; our algorithms combine these approaches…
An algorithm is proposed for constructing directed spanning forests of the minimum weight, in which the maximum possible degree of affinity between the minimum forests is preserved when the number of trees changes. The correctness of the…
The global structure of the minimal spanning tree (MST) is expected to be universal for a large class of underlying random discrete structures. However, very little is known about the intrinsic geometry of MSTs of most standard models, and…
In this paper we present a novel algorithm for concurrent lock-free internal binary search trees (BST) and implement a Set abstract data type (ADT) based on that. We show that in the presented lock-free BST algorithm the amortized step…
This paper makes two main contributions: The first is the construction of a near-minimum spanning tree with constant average distortion. The second is a general equivalence theorem relating two refined notions of distortion: scaling…
Motivated by applications to sensor networks, as well as to many other areas, this paper studies the construction of minimum-degree spanning trees. We consider the classical node-register state model, with a weakly fair scheduler, and we…
We study the problem of privately releasing an approximate minimum spanning tree (MST). Given a graph $G = (V, E, \vec{W})$ where $V$ is a set of $n$ vertices, $E$ is a set of $m$ undirected edges, and $ \vec{W} \in \mathbb{R}^{|E|} $ is an…
Network interdiction problems are a natural way to study the sensitivity of a network optimization problem with respect to the removal of a limited set of edges or vertices. One of the oldest and best-studied interdiction problems is…
We give a new data structure for the fully-dynamic minimum spanning forest problem in simple graphs. Edge updates are supported in $O(\log^4n/\log\log n)$ amortized time per operation, improving the $O(\log^4n)$ amortized bound of Holm et…
Meshless methods are used to solve partial differential equations by approximating differential operators at a node as a weighted sum of values at its neighbours. One of the algorithms for generating nodes suitable for meshless numerical…
In this paper, we study batch parallel algorithms for the dynamic connectivity problem, a fundamental problem that has received considerable attention in the sequential setting. The most well known sequential algorithm for dynamic…
We give the first almost-linear time algorithms for several problems in incremental graphs including cycle detection, strongly connected component maintenance, $s$-$t$ shortest path, maximum flow, and minimum-cost flow. To solve these…
This paper presents a novel approach to enhance the Binary-Addition-Tree algorithm (BAT) by integrating incremental learning techniques. BAT, known for its simplicity in development, implementation, and application, is a powerful implicit…
The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale parallel computation frameworks and has recently gained a lot of importance, especially in the context of classic graph problems.…