Showing papers on "Prim's algorithm published in 1986"
TL;DR: An asynchronous algori thm is described which determines a spanning tree of the graph and can be favourably compared to the one of Gallagher et al.
36 citations
TL;DR: In this paper, a parallel algorithm for updating a minimum spanning tree requires O(log n) time and O(n 2 ) processors, which is the same as the algorithm described in this paper.
28 citations
TL;DR: A parallel algorithm is described for computing the minimum spanning tree of an undirected, connected and weighted graph withn vertices using a shared-memory single-instruction-stream, multiple-data-stream model of computation which does not allow read or write conflicts.
Abstract: A parallel algorithm is described for computing the minimum spanning tree of an undirected, connected and weighted graph withn vertices. We assume a shared-memory single-instruction-stream, multiple-data-stream model of computation which does not allow read or write conflicts. The algorithm is adaptive in the sense that it usesn1−e processors and runs inO(n1+e) time wheree lies between 0 and 1 and depends on the number of available processors. In view of the obvious Ω(n2) lower bound on the number of operations required to compute a minimum spanning tree, the algorithm is also cost-optimal.
14 citations
TL;DR: This experience indicates that the insertion heuristic had much better performance than the greedy in the minimum spanning tree problem with time window constraints; such constraints alter the computational complexity of even “easy” problems involving routing components.
Abstract: SYNOPTIC ABSTRACTThis paper is concerned with the computational complexity and the design and analysis of algorithms for the minimum spanning tree problem with time window constraints; such constraints alter the computational complexity of even “easy” problems involving routing components. It is shown that the minimum spanning tree problem with time windows is NP-hard. We then develop O(n2) greedy and insertion approximate algorithms for its solution. Finally, we report our computational experience with these algorithms; this experience indicates that the insertion heuristic had much better performance than the greedy.
13 citations
15 Jul 1986
TL;DR: A new parallel algorithm for updating the minimum spanning tree of an n-vertex graph following the addition of a new vertex is presented and is superior to known results on this model.
Abstract: A new parallel algorithm for updating the minimum spanning tree of an n-vertex graph following the addition of a new vertex is presented. The algorithm runs in O(log n) time, using O(n) processors on a concurrent-read-exclusive-write parallel random access machine. The algorithm uses a divide-and-conquer strategy, and is superior to known results on this model, that either obtain O(log n) time performance using O(n2) processors, or employ O(n) processors but have a time complexity of O (log2 n).
13 citations
TL;DR: An O(log n) step algorithm for solving the root-shifting problem using n3 processors on a parallel computer which does not permit concurrent writes but allows concurrent reads is presented.
6 citations