China
Africa
Explore chapters and articles related to this topic
Trees and Cycles
Published in Kenneth H. Rosen, Graphs, Algorithms, and Optimization, 2005
A forest is a graph which need not be connected, but whose every component is a tree. Prim’s algorithm constructs a spanning tree by growing a tree from some initial vertex. Kruskal’s algorithm is quite similar, but it begins with a spanning forest and adds edges until it becomes connected. Initially the forest has n — |G| components and no edges. Each component is a single vertex. On each iteration, an edge which connects two distinct components is added, and the two components are merged. When the algorithm terminates the forest has become a tree.
Network Analysis
Published in Michael W. Carter, Camille C. Price, Ghaith Rabadi, Operations Research, 2018
Michael W. Carter, Camille C. Price, Ghaith Rabadi
The complexity of Prim’s algorithm is O(n2) for an n-node network. If the network is sparse (with much less than n2 arcs), the performance of this algorithm on large networks is unnecessarily slow. For such cases, we have an alternative algorithm, known as Kruskal’s algorithm, whose performance is O(e log e) where e is the number of arcs. Thus, in a sparse network where e is much less than n2, Kruskal’s algorithm is superior; whereas in dense networks, Prim’s algorithm is preferred.
Basic Algorithmic Techniques
Published in Charles J. Alpert, Dinesh P. Mehta, Sachin S. Sapatnekar, Handbook of Algorithms for Physical Design Automation, 2008
Vishal Khandelwal, Ankur Srivastava
Unlike Kruskal’s algorithm, that maintains multiple trees and merges them iteratively, Prim’s algorithm has only one tree and merges more vertices in this tree till the MST is created. The algorithm is outlined as follows: Prim(G = (V,E)) Start with any vertex in V and assign it to a Tree T While there exist vertices in G not in T Find a vertex in G-T which is closest to T Expand T by including this vertex
Construction of the developing connecting tree
Published in Engineering Optimization, 2021
Valery M. Kirzhner, Elena V. Ravve, Zeev Volkovich
As is well known, cf. Prim (1957), the Prim algorithm for constructing the minimum spanning tree consists of, at each step, linking the vertex nearest to the constructed fragment. So the Prim algorithm determines an order of linking vertices (Prim's order).
Dynamic routing optimization with electric vehicles under stochastic battery depletion
Published in Transportation Letters, 2022
Volkan Ünal, Mehmet Soysal, Mustafa Çimen, Çağrı Koç
Here, we propose a new solution approach that enhances the RDP logic using Prim’s Algorithm. Prim’s Algorithm is a graph theory method to find the Minimum Spanning Tree (MST) for undirected and connected graphs (Iqbal et al. 2017).