Showing papers on "Prim's algorithm published in 1988"

Pitfalls in the design of distributed routing algorithms

Abstract: The bridge algorithm adopted by the IEEE 802.1 committee for interconnecting 802 LANs requires the topology of the Extended LAN to be a Spanning Tree. A distributed algorithm to compute a spanning tree dynamically has already been published [1], and adopted by the IEEE 802.1 committee [2]. In this paper, however, we describe an alternative distributed algorithm to compute a spanning tree. This algorithm, variants of which have been implemented, initially appears simpler than the IEEE 802.1 algorithm; we show, however, that it has subtle failure modes that makes it unattractive in practice.We also show that some failure modes of the Spanning Tree Algorithm introduced in this paper are characteristic of a broader class of distributed graph algorithms. Such algorithms potentially examine all possible path combinations between a source and destination in a graph. Thus, they suffer from exponential message overhead in topologies that have an exponential number of paths between source and destination. Attempts to fix this problem lead to extra complexity (in terms of CPU, bandwidth, memory) when compared to other algorithms. We briefly describe a second example belonging to this class, and propose that designers avoid such algorithms if restricting the topology or scale of the network is unacceptable.

Minimum augmentation of a tree to a k- edge-connected graph

Abstract: This paper solves the minimum augmentation problem for a given tree and positive integer k, that is, to make a tree k-edge-connected by adding the minimum number of edges. It is shown that the minimum number of edges is the least integer not less than a half of the deficiency of the tree which is defined as the sum of k-(degree) over all the vertices whose degrees are less than k. The proof is constructive and gives a polynomial-time algorithm for constructing such an augmentation.

DFS Tree Construction: Algorithms and Characterizations

Abstract: The Depth First Search (DFS) algorithm is one of the basic techniques which is used in a very large variety of graph algorithms. Every application of the DFS involves, beside traversing the graph, constructing a special structured tree, called a DFS tree. In this paper, we give a complete characterization of all the graphs in which every spanning tree is a DFS tree. These graphs are called Total-DFS-Graphs. The characterization we present shows that a large variety of graphs are not Total-DFS-Graphs, and therefore the following question is naturally raised: Given an undirected graph G=(V,E) and an undirected spanning tree T, is T a DFS tree of G? We give an algorithm to answer this question in linear (O(|E|)) time.

A new node-join-tree distributed algorithm for minimum weight spanning trees

Abstract: A distributed algorithm that uses a node-join-tree approach for the minimum-spanning-tree problem in a communication network is developed. The algorithm needs at most (2e+n(n-1)/4) messages in O(n/sup 2/) time on a general random graph. In the best case, it needs only 2e messages in O(log n) time. The parameters e and n are the number of edges and nodes, respectively. Although the worst-case performance is not better than that of tree-join-tree algorithms under some extreme cases, simulation results show that it provides better performance in most cases. The algorithm is initialized from a single node, so that there is no need to wake up all nodes at the beginning. It is less complicated than other algorithms, so that a reliable implementation is easier to achieve. The results can be used to improve the algorithms for many other problems in distributed computing, such as leader-election, node-counting, deadlock-resolution, and message-broadcasting. >

Minimum Spanning Tree Algorithm On An Image Understanding Architecture

Abstract: A parallel algorithm for computing the minimum spanning tree of a weighted, undirected graph on an n x n mesh-connected array with a special "gated connection network" is presented. For a graph of n vertices, the algorithm requires O(log2n) time. At each step in the parallel algorithm, each node selects one of its links with the least cost as a spanning tree link. Linked nodes form connected components, so that each node eventually belongs to a group with its own identity. The connected components and their associated indices are then treated as super nodes at the next minimum link determination step. The gated connection network function is to allow all the nodes within a connected component to be electrically connected, regardless of where they are located in the adjacency matrix. The index or label used for that component is the local minimum of the node index. All the connected component operations, and those for finding minimum links between them, can be performed in parallel.