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.

Distributed Algorithms for Minimum Spanning Trees.

Abstract: Consider a communication network, modeled by an undirected weighted graph G D .V; E/, where jV j D n; jEj D m. Each vertex of V represents a processor of unlimited computational power; the processors have unique identity numbers (ids), and they communicate via the edges of E by sending messages to each other. Also, each edge e 2 E has associated a weight w.e/, known to the processors at the endpoints of e. Thus, a processor knows which edges are incident to it and their weights, but it does not know any other information about G. The network is asynchronous: each processor runs at an arbitrary speed, which is independent of the speed of other processors. A processor may wake up spontaneously or when it receives a message from another processor. There are no failures in the network. Each message sent arrives at its destination within a finite but arbitrary delay. A distributed algorithm A for G is a set of local algorithms, one for each processor of G, that include instructions for sending and receiving messages along the edges of the network. Assuming that A terminates (i.e., all the local algorithms eventually terminate), its message complexity is the total number of messages sent over any execution of the algorithm, in the worst case. Its time complexity is the worst-case execution time, assuming processor steps take negligible time, and message delays are normalized to be at most 1 unit. A minimum spanning tree (MST) of G is a subset E 0 of E such that the graph T D .V; E 0/ is a tree (connected and acyclic) and its total weight, w.E 0/ D P e2E0 w.e/, is as small as possible.

A Minimum Cut Algorithm Using Maximum Adjacency Merging Method of Undirected Graph

Abstract: Given weighted graph  , the minimum cut problem is classified with source  and sink  or without  and  . Given undirected weighted graph without  and  , Stoer-Wagner algorithm is most popular. This algorithm fixes arbitrary vertex, and arranges maximum adjacency (MA)-ordering. In the last, the sum of weights of the incident edges for last ordered vertex is computed by cut value, and the last 2 vertices are merged. Therefore, this algorithm runs  times. Given graph with  and  , Ford-Fulkerson algorithm determines the bottleneck edges in the arbitrary augmenting path from  to  . If the augmenting path is no more exist, we determine the minimum cut value by combine the all of the bottleneck edges. This paper suggests minimum cut algorithm for undirected weighted graph with  and  . This algorithm suggests MA-merging and computes cut value simultaneously. This algorithm runs  times and successfully divides  into disjoint  and  sets on the basis of minimum cut, but the Stoer-Wagner is fails sometimes. The proposed algorithm runs more than Ford-Fulkerson algorithm, but finds the minimum cut value within

A fault-tolerant token passing algorithm on tree networks

Abstract: We present a self stabilizing token passing algorithm for a tree network. The algorithm is based on the 4 state mutual exclusion algorithm of E.W. Dijkstra (1974) and works under the distributed daemon model of execution. Although our algorithm relies upon an underlying tree network topology, it is not less general than the protocol by S. Huang and N. Chen (1993) since a spanning tree of a network can be obtained by a number of self stabilizing algorithms (A. Arora and M. Gouda, 1993; N. Chen et al., 1991; S. Huang and N. Chen, 1992; S. Sur and P.K. Srimani, 1992). Token passing on a spanning tree thus places no restriction on the topology of the underlying distributed system.

Divide-and-conquer minimal-cut bisectioning of task graphs

Abstract: This paper proposes a method for partitioning the vertex set of an undirected simple weighted graph into two subsets so as to minimise the difference of vertex-weight sums between the two subsets and the total weight of edges cut (i.e., edges with one end in each subset). The proposed heuristic algorithm works in a divide-and-conquer fashion and is a modification of an algorithm suggested in the literature. The algorithm has the same time complexity as the previous one but is extended to work on weighted graphs. >

MOD-CHAR: An Implementation of Char's Spanning Tree Enumeration Algorithm and Its Complexity Analysis

Abstract: Abstruct -An implementation, called MOD-CHAR, of Char’s spanning tree enumeration algorithm [3] is discussed. Two complexity analyses of MOD-CHAR are presented. It is shown that MOD-CHAR leads to better complexity results for Char’s algorithm than what could be obtained using the straightforward implementation implied in Char’s original presentation 131. The class of graphs for which MOD-CHAR and, hence, Char’s algorithm has linear time complexity per spanning tree generated is identified. This class is more general than the corresponding one identified in [7J. Using a result due to Matula [lo], [12] on random graphs, it is proved that for almost all graphs MOD-CHAR has linear worst-case time complexity per spanning tree generated. It is also shown that for any complete graph MOD-CHAR requires, on the average, at most seven computational steps to generate a spanning tree. This result and computational experiences provide evidence to believe that for dense graphs of any order the time complexity of MOD-CHAR is O( t), where t is the number of spanning trees generated. On the other hand, there is enough evidence to conclude that for sparse graphs, Char’s original implementation is superior to MOD-CHAR.