Prim's algorithm

About: Prim's algorithm is a research topic. Over the lifetime, 775 publications have been published within this topic receiving 17971 citations. The topic is also known as: DJP algorithm & Jarník algorithm.

Optimal Parallel and Sequential Algorithms for the Vertex Updating Problem of a Minimum Spanning Tree

Abstract: We present a set of rules that can be used to give optimal solutions to the vertex updating problem for a minimum spanning tree: Update a given MST when a new vertex z is introducted, along with weighted edges that connect z with the vertices of the graph. These rules lead to simple parallel algorithms that run in O(lg n) parallel time using n/lg n EREW PRAMs. They can also be used to derive simple linear-time sequential algorithms for the same problem. Furthermore, we show how our solution can be used to solve the multiple vertex updating problem.

Functional Correctness of C implementations of Dijkstra’s, Kruskal’s, and Prim’s Algorithms

Abstract: We develop machine-checked verifications of the full functional correctness of C implementations of the eponymous graph algorithms of Dijkstra, Kruskal, and Prim. We extend Wang et al.’s CertiGraph platform to reason about labels on edges, undirected graphs, and common spatial representations of edge-labeled graphs such as adjacency matrices and edge lists. We certify binary heaps, including Floyd’s bottom-up heap construction, heapsort, and increase/decrease priority.

Determining minimum spanning tree in an undirected weighted graph

Abstract: This paper proposed a new algorithm to find a minimum spanning tree of an undirected weighted graph graph This new algorithm provides a fresh approach to produce a minimum spanning tree A minimum spanning tree is a sub graph of any undirected weighted graph that gives the minimal cost valued edges to reach every node of any graph The proposed algorithm is named as RAY algorithm for determining the minimum spanning tree We named this new algorithm as RAY, as it gives a new ray of hope in the field of graphs that can be used as a better option for finding the minimum spanning tree of any undirected weighted graph with less duration of time as well as with an easy approach RAY has less complexity with respect to time for finding the minimum spanning tree of any graph in comparison to other algorithms like prim's algorithm and Kruskal's algorithm which are mostly used to find a minimum spanning tree of the graph RAY algorithm select any one node of the given graph as a root node and then it joins every edge connected to that node, which do not form any cycle in the graph This process is repeated until we traverse each node of the graph and the edges those forms cycle during this process are stored separately Now only these separately stored edges are traversed and we check in the graph for maximum weighted edge from the edges that are coming in the cycle which is formed due that particular separately stored edge If there is any edge in the cycle which is greater in weigh than that of separately stored edge then we discarded maximum weighted edge and the new edge which we stored separately is taken into the minimum spanning tree This same procedure is repeated for each edge that we stored separately At the end of this procedure we get a tree which is the minimum spanning tree of the given graph by using RAY algorithm