A linear algorithm for centering a spanning tree of a biconnected graph (original) (raw)
Related papers
Centering a spanning tree of a biconnected graph
Information Processing Letters, 1989
Given a biconnected graph G = (V, E), and an arbitrary vertex v in V, there exists a spanning tree T of G with v in the center of T. We prove this by providing an O( 1 V 1. 1 E I) algorithm that constructs such a tree.
On central spanning trees of a graph
Lecture Notes in Computer Science, 1996
We consider the collection of all spanning trees of a graph with distance between them based on the size of the symmetric difference of their edge sets. A central spanning tree of a graph is one for which the maximal distance to all other spanning trees is minimal. We prove that the problem of constructing a central spanning tree is algorithmically difficult and leads to an NP-complete problem.
HAL (Le Centre pour la Communication Scientifique Directe), 2019
We propose a new algorithm for finding the center of a graph, as well as the rank of each node in the hierarchy of distances to the center. In other words, our algorithm allows to partition the graph according to nodes distance to the center. Moreover, the algorithm is parallelizable. We compare the performances of our algorithm with the ones of Floyd-Warshall algorithm, which is traditionally used for these purposes. We show that, for a large variety of graphs, our algorithm outperforms the Floyd-Warshall algorithm.
On the minimum diameter spanning tree problem
Information Processing Letters, 1995
We point out a relation between the minimum diameter spanning tree of a graph and its absolute 1-center. We use this relation to solve the diameter problem and an extension of it efficiently.
A distributed algorithm for constructing a minimum diameter spanning tree
2004
We present a new algorithm, which solves the problem of distributively finding a mini-mum diameter spanning tree of any (non-negatively) real-weighted graph G = (V,E, ω). As an intermediate step, we use a new, fast, linear-time all-pairs shortest paths distributed algo-rithm to find an absolute center of G. The resulting distributed algorithm is asynchronous, it works for named asynchronous arbitrary networks and achieves O(|V |) time complexity and O (|V | |E|) message complexity.
A Linear Time Algorithm for Finding Minimum Spanning Tree Replacement Edges
ArXiv, 2019
Given an undirected, weighted graph, the minimum spanning tree (MST) is a tree that connects all of the vertices of the graph with minimum sum of edge weights. In real world applications, network designers often seek to quickly find a replacement edge for each edge in the MST. For example, when a traffic accident closes a road in a transportation network, or a line goes down in a communication network, the replacement edge may reconnect the MST at lowest cost. In the paper, we consider the case of finding the lowest cost replacement edge for each edge of the MST. A previous algorithm by Tarjan takes O(malpha(m,n))O(m \alpha(m, n))O(malpha(m,n)) time, where alpha(m,n)\alpha(m, n)alpha(m,n) is the inverse Ackermann's function. Given the MST and sorted non-tree edges, our algorithm is the first that runs in O(m+n)O(m+n)O(m+n) time and O(m+n)O(m+n)O(m+n) space to find all replacement edges. Moreover, it is easy to implement and our experimental study demonstrates fast performance on several types of graphs. Additionally, since the most vital edg...
On finding spanning trees with few leaves
2008
The problem of finding a spanning tree with few leaves is motivated by the design of communication networks, where the cost of the devices depends on their routing functionality (ending, forwarding, or routing a connection). Besides this application, the problem has its own theoretical importance as a generalization of the Hamiltonian path problem. Lu and Ravi showed that there is no constant factor approximation for minimizing the number of leaves of a spanning tree, unless P = NP. Thus instead of minimizing the number of leaves, we are going to deal with maximizing the number of non-leaves: we give a linear-time 2-approximation for arbitrary graphs, a 3/2-approximation for claw-free graphs, and a 6/5-approximation for cubic graphs.
An analysis between exact and approximate algorithms for the k-center problem in graphs
International Journal of Electrical and Computer Engineering (IJECE), 2022
This research focuses on the k-center problem and its applications. Different methods for solving this problem are analyzed. The implementations of an exact algorithm and of an approximate algorithm are presented. The source code and the computation complexity of these algorithms are presented and analyzed. The multitasking mode of the operating system is taken into account considering the execution time of the algorithms. The results show that the approximate algorithm finds solutions that are not worse than two times optimal. In some case these solutions are very close to the optimal solutions, but this is true only for graphs with a smaller number of nodes. As the number of nodes in the graph increases (respectively the number of edges increases), the approximate solutions deviate from the optimal ones, but remain acceptable. These results give reason to conclude that for graphs with a small number of nodes the approximate algorithm finds comparable solutions with those founds by...
Complex & Intelligent Systems
Generation of all possible spanning trees of a graph is a major area of research in graph theory as the number of spanning trees of a graph increases exponentially with graph size. Several algorithms of varying efficiency have been developed since early 1960s by researchers around the globe. This article is an exhaustive literature survey on these algorithms, assuming the input to be a simple undirected connected graph of finite order, and contains detailed analysis and comparisons in both theoretical and experimental behavior of these algorithms.
IJERT-Minimum Spanning Tree Of Undirected Graphs
International Journal of Engineering Research and Technology (IJERT), 2012
https://www.ijert.org/minimum-spanning-tree-of-undirected-graphs https://www.ijert.org/research/minimum-spanning-tree-of-undirected-graphs-IJERTV1IS10238.pdf This paper presents an approach to finding the minimum spanning tree for simple undirected graphs and undirected multi-graphs. The algorithm involves choosing the minimum edge that connects each disjoint component of the graph, until a single component is formed. This single component is the minimum spanning tree of the given graph. The approach we take is a slight modification to Sollin's algorithm.