Related papers: Memory-Efficient Solutions to Large-Graph MST Prob…
Memory-(in)efficiency is a crucial consideration that oftentimes prevents deployment of state-of-the-art distributed algorithms in real-life modern networks. In the context of the MST problem, roughly speaking, there are three types of…
Minimum spanning trees (MSTs) provide a convenient representation of datasets in numerous pattern recognition activities. Moreover, they are relatively fast to compute. In this paper, we quantify the extent to which they are meaningful in…
We present Fast Approximate Minimum Spanning Tree (FAMST), a novel algorithm that addresses the computational challenges of constructing Minimum Spanning Trees (MSTs) for large-scale and high-dimensional datasets. FAMST utilizes a…
We develop and extensively evaluate highly scalable distributed-memory algorithms for computing minimum spanning trees (MSTs). At the heart of our solutions is a scalable variant of Boruvka's algorithm. For partitioned graphs with many…
We consider the Steiner tree problem on graphs where we are given a set of nodes and the goal is to find a tree sub-graph of minimum weight that contains all nodes in the given set, potentially including additional nodes. This is a…
The Multiobjective Minimum Spanning Tree (MO-MST) problem is a variant of the Minimum Spanning Tree problem, in which the costs associated with every edge of the input graph are vectors. In this paper, we design a new dynamic programming…
The minimum-cost arborescence problem is a well-studied problem in the area of graph theory, with known polynomial-time algorithms for solving it. Previous literature introduced new variations on the original problem with different…
Finding a minimum spanning tree (MST) for $n$ points in an arbitrary metric space is a fundamental primitive for hierarchical clustering and many other ML tasks, but this takes $\Omega(n^2)$ time to even approximate. We introduce a…
We present improved learning-augmented algorithms for finding an approximate minimum spanning tree (MST) for points in an arbitrary metric space. Our work follows a recent framework called metric forest completion (MFC), where the learned…
Given a set of points in the Euclidean plane, the Euclidean \textit{$\delta$-minimum spanning tree} ($\delta$-MST) problem is the problem of finding a spanning tree with maximum degree no more than $\delta$ for the set of points such the…
In this paper, we present a fully-dynamic distributed algorithm for maintaining a minimum spanning tree on general graphs with positive real edge weights. The goal of a dynamic MST algorithm is to update efficiently the minimum spanning…
The Minimum Spanning Tree Problem with Conflicts consists in finding the minimum conflict-free spanning tree of a graph, i.e., the spanning tree of minimum cost, including no pairs of edges that are in conflict. In this paper, we solve this…
We develop fast approximation algorithms for the minimum-cost version of the Bounded-Degree MST problem (BD-MST) and its generalization the Crossing Spanning Tree problem (Crossing-ST). We solve the underlying LP to within a $(1+\epsilon)$…
Robust optimization is a widely studied area in operations research, where the algorithm takes as input a range of values and outputs a single solution that performs well for the entire range. Specifically, a robust algorithm aims to…
Quantum algorithms for several problems in graph theory are considered. Classical algorithms for finding the lowest weight path between two points in a graph and for finding a minimal weight spanning tree involve searching over some space.…
The semi-streaming model is a variant of the streaming model frequently used for the computation of graph problems. It allows the edges of an $n$-node input graph to be read sequentially in $p$ passes using $\tilde{O}(n)$ space. In this…
We consider the minimum spanning tree (MST) problem under the restriction that for every vertex v, the edges of the tree that are adjacent to v satisfy a given family of constraints. A famous example thereof is the classical…
With applications in distribution systems and communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The…
The seminal work of Ahn, Guha, and McGregor in 2012 introduced the graph sketching technique and used it to present the first streaming algorithms for various graph problems over dynamic streams with both insertions and deletions of edges.…
In this article, we study the Euclidean minimum spanning tree problem in an imprecise setup. The problem is known as the \emph{Minimum Spanning Tree Problem with Neighborhoods} in the literature. We study the problem where the neighborhoods…