Related papers: New Algorithms for Incremental Minimum Spanning Tr…
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…
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…
For a given graph $G$, a maximum internal spanning tree of $G$ is a spanning tree of $G$ with maximum number of internal vertices. The Maximum Internal Spanning Tree (MIST) problem is to find a maximum internal spanning tree of the given…
Traditional decision tree models, which rely exclusively on numerical variables, often face challenges in handling high-dimensional data and are limited in their ability to incorporate textual information effectively. To address these…
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…
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…
One popular technique to solve temporal planning problems consists in decoupling the causal decisions, demanding them to heuristic search, from temporal decisions, demanding them to a simple temporal network (STN) solver. In this…
In this paper we study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an $n$-vertex graph $G=(V,E,w)$ with positive real edge weights, and our goal is to maintain a tree which is a good…
We consider the ``minimum degree spanning tree'' problem. As input, we receive an undirected, connected graph $G=(V, E)$ with $n$ nodes and $m$ edges, and our task is to find a spanning tree $T$ of $G$ that minimizes $\max_{u \in V}…
Graph pattern matching algorithms to handle million-scale dynamic graphs are widely used in many applications such as social network analytics and suspicious transaction detections from financial networks. On the other hand, the computation…
We consider a family of local search algorithms for the minimum-weight spanning tree, indexed by a parameter $\rho$. One step of the local search corresponds to replacing a connected induced subgraph of the current candidate graph whose…
Distributed graph algorithms that separately optimize for either the number of rounds used or the total number of messages sent have been studied extensively. However, algorithms simultaneously efficient with respect to both measures have…
We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m^{1+o(1)}$ time. This improves on the previous best bound of…
For many algorithmic problems, traditional algorithms that optimise on the number of instructions executed prove expensive on I/Os. Novel and very different design techniques, when applied to these problems, can produce algorithms that are…
There are numerous randomized algorithms to generate spanning trees in a given ambient graph; several target the uniform distribution on trees (UST), while in practice the fastest and most frequently used draw random weights on the edges…
Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios, often requiring intricate algorithmic design and exponential time. Recently, there has been growing interest in end-to-end deep neural…
Although spatio-temporal graph neural networks have achieved great empirical success in handling multiple correlated time series, they may be impractical in some real-world scenarios due to a lack of sufficient high-quality training data.…
This paper investigates the execution of tree-shaped task graphs using multiple processors. Each edge of such a tree represents a large IO file. A task can only be executed if all input and output files fit into memory, and a file can only…
In the classical Steiner tree problem, given an undirected, connected graph $G=(V,E)$ with non-negative edge costs and a set of \emph{terminals} $T\subseteq V$, the objective is to find a minimum-cost tree $E' \subseteq E$ that spans the…
The Steiner tree problem aims to determine a minimum edge-weighted tree that spans a given set of terminal vertices from a given graph. In the past decade, a considerable number of algorithms have been developed to solve this…