Showing papers on "Prim's algorithm published in 1992"
TL;DR: This paper describes a linear-time algorithm for verifying a minimum spanning tree and combines the result of Komlos with a preprocessing and table look-up method for small subproblems and with a previously known almost-linear- time algorithm.
Abstract: Komlos has devised a way to use a linear number of binary comparisons to test whether a given spanning tree of a graph with edge costs is a minimum spanning tree. The total computational work required by his method is much larger than linear, however. This paper describes a linear-time algorithm for verifying a minimum spanning tree. This algorithm combines the result of Komlos with a preprocessing and table look-up method for small subproblems and with a previously known almost-linear-time algorithm. Additionally, an optimal deterministic algorithm and a linear-time randomized algorithm for sensitivity analysis of minimum spanning trees are presented.
152 citations
TL;DR: In this paper, an edge-ordered dynamic tree (EDDT) data structure is proposed for maintaining a minimum spanning forest of a plane graph subject to on-line modifications, such as changes in the edge weights and insertion and deletion of edges and vertices which are consistent with the given embedding.
124 citations
01 Jun 1992
TL;DR: A simple and implementable algorithm that computes a minimum spanning tree of an undirected weighted graph G = (V;E) of n = jV j vertices andm = jEj edges on an EREW PRAM in O(log3=2n) time using n+m processors is presented.
Abstract: We present a simple and implementable algorithm that computes a minimum spanning tree of an undirected weighted graph G = (V;E) of n = jV j vertices andm = jEj edges on an EREW PRAM in O(log3=2n) time using n+m processors. This represents a substantial improvement in the running time over the previous results for this problem using at the same time the weakest of the PRAM models. It also implies the existence of algorithms having the same complexity bounds for the EREW PRAM, for connectivity, ear decomposition, biconnectivity, strong orientation, st-numbering and Euler tours problems.
67 citations
19 Jun 1992
TL;DR: A simple but efficient (O(n + m ln n)) algorithm to test the primality of undirected graphs and can be seen as a common generalization of Spinrad's work on P4-tree structure and substitution decomposition and Ille's one about the structure of prime graphs.
Abstract: A graph is said to be prime if it has no non-trivial substitution decomposition, or module This paper introduces a simple but efficient (O(n + m ln n)) algorithm to test the primality of undirected graphs The fastest previous algorithm is due to Muller and Spinrad [MS89] and requires quadratic time Our approach can be seen as a common generalization of Spinrad's work on P4-tree structure and substitution decomposition [Spi89] and Ille's one about the structure of prime graphs [Ill90] (see also Schmerl and Trotter [ST91] which contains similar results)
37 citations
03 Feb 1992
TL;DR: A transitive closure algorithm that maintains a spanning tree of successors for each node rather than a simple successor list is presented, which promotes sharing of information across multiple nodes and leads to more efficient algorithms.
Abstract: The authors present a transitive closure algorithm that maintains a spanning tree of successors for each node rather than a simple successor list. This spanning tree structure promotes sharing of information across multiple nodes and leads to more efficient algorithms. An effective relational implementation of the spanning tree storage structure is suggested, and it is shown how blocking can be applied to reduce the input/output cost of the algorithm. The algorithm can handle path problems also. Analytical and experimental evidence is presented that demonstrates the utility of the algorithm, especially in a graph with many alternate paths between the nodes. The spanning tree storage structure can be compressed and updated incrementally in response to changes in the underlying graph. >
20 citations
Proceedings Article•
01 Jan 1992
14 citations
TL;DR: A system for visualizing correctness proofs of graph algorithms and is particularly appropriate for greedy algorithms, though much of what is discussed can guide visualization of proofs in other contexts.
Abstract: In this paper we describe a system for visualizing correctness proofs of graph algorithms. The system has been demonstrated for a greedy algorithm. Prim?s algorithm for finding a minimum spanning tree of an undirected, weighted graph. We believe that our system is particularly appropriate for greedy algorithms, though much of what we discuss can guide visualization of proofs in other contexts. While an example is not a proof, our system provides concrete examples to illustrate the operation of the algorithm. These examples can be referred to by the user interactively and alternatively with the visualization of the proof where the general case is portrayed abstractly.
4 citations
01 Apr 1992
TL;DR: A parallel algorithm for constructing a minimum spanning tree of a connected, weighted, undirected graph in O(log m) time using O(m + n) processors is presented for an SIMD machine.
Abstract: A parallel algorithm for constructing a minimum spanning tree of a connected, weighted, undirected graph in O(log m) time using O(m + ) processors is presented for an SIMD machine where m and n denote the number of edges and vertices respectively.
2 citations
TL;DR: A parallel algorithm for computing a furthest neighbor of each vertex in a tree of size n with positive (real-valued) edge weights and it is shown that all furthest neighbors of all vertices can also be computed within the same resource bounds.
1 citations
TL;DR: The spanning tree maintenance problem for an LAN model in which node processors may halt and recover is considered and an algorithm meeting the conditions that the spanning tree is an L-ary complete tree and that nodes halt or recover singly is presented.
Abstract: The spanning tree maintenance problem for an LAN model in which node processors may halt and recover is considered. An algorithm meeting the conditions that the spanning tree is an L-ary complete tree and that nodes halt or recover singly is presented. The message complexity of this algorithm is shown to be comparable with local computational complexity
1 citations
TL;DR: A new linear algorithm for coloring the edges of a tree that unlike the existing ones can be parallelized directly and can be extended very easily without increasing the resource requirement.
01 Mar 1992
TL;DR: An efficient parallel algorithm for constructing a breadth-first spanning tree of an interval graph based on elegantly capturing the structure of a given collection of intervals is designed, which is found to be instrumental in solving many other problems including the computation of a depth-depth spanning tree.
Abstract: The authors design an efficient parallel algorithm for constructing a breadth-first spanning tree of an interval graph. Their novel approach is based on elegantly capturing the structure of a given collection of intervals. This structure reveals important properties of the corresponding interval graph, and is found to be instrumental in solving many other problems including the computation of a breadth-depth spanning tree, which they report for the first time. The algorithm requires O(logn) time employing O(n) processors on the EREW PRAM model. >