scholarly journals IMPLEMENTASI ALGORITMA KRUSKAL DAN ALGORITMA PRIM SUATU GRAPH DENGAN APLIKASI BERBASIS DESKTOP

2020 ◽  
Vol 3 (2) ◽  
pp. 89-93
Author(s):  
Siti Alvi Sholikhatin ◽  
Adi Budi Prasetyo ◽  
Ade Nurhopipah
Keyword(s):  
Spanning Tree ◽  
Research Study ◽  
Minimum Spanning Tree ◽  
Greedy Algorithms ◽  
Relevant Literature ◽  
Weighted Graph ◽  
Self Assessment ◽  
Technological Readiness ◽  
Actual Environment ◽  
Application Design

A graph has several algorithms in its solution, including the Kruskal algorithm and Prim algorithm, both of which are greedy algorithms for determining the minimum spanning tree. Completion of graphs is useful in various fields of life, so an accurate graph calculation is important. Making an application to solve a graph, especially the Kruskal algorithm and Prim algorithm aims to facilitate the work of the graph so as to produce an accurate final result. The flow of research carried out are: a background review of research, study of literature and relevant literature, application design, building desktop-based applications, as well as implementation and application tests. The level of technological readiness or TKT in this research is based on self-assessment which is at level 7, meaning the prototype demonstration system in the actual environment, with details of the TKT indicators as follows: TKT indicator 1 is met, TKT indicator 2 is met, TKT indicator 3 is not met, TKT indicator 4, TKT indicator 5 are met, TKT indicator 6 are met, TKT indicator 7 is met, TKT indicator 8 and 9 are not met. The application that has been built is useful for completing a graph with the Kruskal algorithm and Prim algorithm. This research was conducted to answer the crucial needs of a weighted graph settlement application.

scholarly journals A Constant-Factor Approximation for the Generalized Cable-Trench Problem

2019 ◽  
Author(s):  
Marcelo Benedito ◽  
Lehilton Pedrosa ◽  
Hugo Rosado
Keyword(s):  
Shortest Path ◽  
Steiner Tree ◽  
Spanning Tree ◽  
Optimization Problem ◽  
Minimum Spanning Tree ◽  
Weighted Graph ◽  
Constant Factor ◽  
Steiner Tree Problem ◽  
Negative Factor ◽  
Path Lengths

In the Cable-Trench Problem (CTP), the objective is to find a rooted spanning tree of a weighted graph that minimizes the length of the tree, scaled by a non-negative factor , plus the sum of all shortest-path lengths from the root, scaled by another non-negative factor. This is an intermediate optimization problem between the Single-Destination Shortest Path Problem and the Minimum Spanning Tree Problem. In this extended abstract, we consider the Generalized CTP (GCTP), in which some vertices need not be connected to the root, but may serve as cost-saving merging points; this variant also generalizes the Steiner Tree Problem. We present an 8.599-approximation algorithm for GCTP. Before this paper, no constant approximation for the standard CTP was known.

On the Euclidean Minimum Spanning Tree Problem

2005 ◽  
Vol 1 (1) ◽  
pp. 11-14 ◽  
Author(s):  
Sanguthevar Rajasekaran
Keyword(s):  
Spanning Tree ◽  
Euclidean Distance ◽  
Minimum Spanning Tree ◽  
Linear Time ◽  
Randomized Algorithm ◽  
Weighted Graph ◽  
Deterministic Algorithm ◽  
Probabilistic Algorithms ◽  
Tree Algorithms ◽  
Minimum Spanning Tree Problem

Given a weighted graph G(V;E), a minimum spanning tree for G can be obtained in linear time using a randomized algorithm or nearly linear time using a deterministic algorithm. Given n points in the plane, we can construct a graph with these points as nodes and an edge between every pair of nodes. The weight on any edge is the Euclidean distance between the two points. Finding a minimum spanning tree for this graph is known as the Euclidean minimum spanning tree problem (EMSTP). The minimum spanning tree algorithms alluded to before will run in time O(n2) (or nearly O(n2)) on this graph. In this note we point out that it is possible to devise simple algorithms for EMSTP in k- dimensions (for any constant k) whose expected run time is O(n), under the assumption that the points are uniformly distributed in the space of interest.CR Categories: F2.2 Nonnumerical Algorithms and Problems; G.3 Probabilistic Algorithms

Clustering Vertices in Weighted Graphs

2011 ◽  
pp. 285-298
Author(s):  
Derry Tanti Wijaya ◽  
Stephane Bressan
Keyword(s):  
Graph Algorithms ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Weighted Graph ◽  
Graph Clustering ◽  
Weighted Graphs ◽  
Similarity Relations ◽  
Natural Notion ◽  
Cluster Density ◽  
Markov Clustering

Clustering is the unsupervised process of discovering natural clusters so that objects within the same cluster are similar and objects from different clusters are dissimilar. In clustering, if similarity relations between objects are represented as a simple, weighted graph where objects are vertices and similarities between objects are weights of edges; clustering reduces to the problem of graph clustering. A natural notion of graph clustering is the separation of sparsely connected dense sub graphs from each other based on the notion of intra-cluster density vs. inter-cluster sparseness. In this chapter, we overview existing graph algorithms for clustering vertices in weighted graphs: Minimum Spanning Tree (MST) clustering, Markov clustering, and Star clustering. This includes the variants of Star clustering, MST clustering and Ricochet.

Mathematical Modelling for Transportation With Application to Airline Transportation Network

2021 ◽  
pp. 28-51
Author(s):  
Sadiqah Almarzooq ◽  
Njwd Albishi
Keyword(s):  
Graph Theory ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Transportation Networks ◽  
Transportation Network ◽  
Weighted Graph ◽  
Search Method ◽  
Nearest Neighbour ◽  
Water Pipelines ◽  
Regional Airports

Graph theory is a basic tool to solve real-world problems such as communication between people, water pipelines, and transportation networks. A transportation network can be modeled as connected weighted graph. This chapter starts by introducing some fundamental concepts of graph theory to be applied to three main problems: the minimum spanning tree, the shortest path, and the travel salesperson. The authors discuss some appropriated algorithms such as depth first algorithm, Prim's algorithm, Kruskal's algorithm, Dijkstra's algorithm, the nearest neighbour algorithm, the minimum spanning tree depth first search method (MST-DFS) algorithm, and the Christofides' algorithm to solve these problems and apply them the airlines network between international and regional airports in Saudi Arabia.

NEW METAHEURISTIC APPROACHES FOR THE LEAF-CONSTRAINED MINIMUM SPANNING TREE PROBLEM

2008 ◽  
Vol 25 (04) ◽  
pp. 575-589 ◽  
Author(s):  
ALOK SINGH ◽  
ANURAG SINGH BAGHEL
Keyword(s):  
Genetic Algorithm ◽  
Tabu Search ◽  
Ant Colony Optimization ◽  
Spanning Tree ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Weighted Graph ◽  
The Other ◽  
Greedy Heuristic ◽  
New Approaches

Given an undirected, connected, weighted graph, the leaf-constrained minimum spanning tree (LCMST) problem seeks a spanning tree of the graph with smallest weight among all spanning trees of the graph, which contains at least l leaves. In this paper we have proposed two new metaheuristic approaches for the LCMST problem. One is an ant-colony optimization (ACO) algorithm, whereas the other is a tabu search based algorithm. Similar to a previously proposed genetic algorithm, these metaheuristic approaches also use the subset coding that represents a leaf-constrained spanning tree by the set of its interior vertices. Our new approaches perform well in comparison with two best heuristics reported in the literature for the problem — the subset-coded genetic algorithm and a greedy heuristic.

scholarly journals ALGORITMA “HANCURKAN SEMUA SIKEL” UNTUK MENENTUKAN POHON PERENTANG MINIMUM DARI SUATU GRAF BERBOBOT

2019 ◽  
Vol 21 (2) ◽  
pp. 91-98
Author(s):  
Ricky Aditya
Keyword(s):  
Graph Theory ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Weighted Graph ◽  
Alternative Algorithm

The minimum spanning tree is one of the applications of graph theory in various fields. There are several algorithms for determining the minimum spanning tree of a weighted graph, such as Kruskal's algorithm and Prim's algorithm. These two algorithms are not really easy to teach to students in general. Therefore in this paper presented an alternative algorithm called the algorithm "Destroy All Sikel", which is more intuitive and easier to understand. Furthermore, there are also examples of implementation and comparison with two other algorithms.

scholarly journals A Note on Ultrametric Spaces, Minimum Spanning Trees and the Topological Distance Algorithm

Information ◽  
2020 ◽  
Vol 11 (9) ◽  
pp. 418
Author(s):  
Jörg Schäfer
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Greedy Algorithms ◽  
Reconstruction Algorithm ◽  
Minimum Spanning Trees ◽  
Ultrametric Spaces ◽  
Correctness Proof ◽  
Topological Distance ◽  
Join Algorithm

We relate the definition of an ultrametric space to the topological distance algorithm—an algorithm defined in the context of peer-to-peer network applications. Although (greedy) algorithms for constructing minimum spanning trees such as Prim’s or Kruskal’s algorithm have been known for a long time, they require the complete graph to be specified and the weights of all edges to be known upfront in order to construct a minimum spanning tree. However, if the weights of the underlying graph stem from an ultrametric, the minimum spanning tree can be constructed incrementally and it is not necessary to know the full graph in advance. This is possible, because the join algorithm responsible for joining new nodes on behalf of the topological distance algorithm is independent of the order in which the nodes are added due to the property of an ultrametric. Apart from the mathematical elegance which some readers might find interesting in itself, this provides not only proofs (and clearer ones in the opinion of the author) for optimality theorems (i.e., proof of the minimum spanning tree construction) but a simple proof for the optimality of the reconstruction algorithm omitted in previous publications too. Furthermore, we define a new algorithm by extending the join algorithm to minimize the topological distance and (network) latency together and provide a correctness proof.

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