Trans-dichotomous algorithms for minimum spanning trees and shortest paths

• Published in: Foundations of Computer Science, 31st Symposium pp. 719 - 725 vol.2
• Main Authors: Fredman, M.L., Willard, D.E.
• Format: Conference Proceeding
• Language: English
• Published: IEEE Comput. Soc. Press 1990
• Subjects: Algorithm design and analysis; Arithmetic; Computational modeling; Concurrent computing; Costs; Data structures; Inference algorithms; Performance evaluation; Tree data structures; Tree graphs
• ISBN: 081862082X; 9780818620829
• DOI: 10.1109/FSCS.1990.89594

The fusion tree method is extended to develop a linear-time algorithm for the minimum spanning tree problem and an O(m+n log n/log log n) implementation of Dijkstra's shortest-path algorithm for a graph with n vertices and m edges. The shortest-path algorithm surpasses information-theoretic limitations. The extension of the fusion tree method involves the development of a new data structure, the atomic heap. The atomic heap accommodates heap (priority queue) operations in constant amortized time under suitable polylog restrictions on the heap size. The linear-time minimum spanning tree algorithm results from a direct application of the atomic heap. To obtain the shortest path algorithm, the atomic heap is used as a building block to construct a new data structure, the AF-heap, which has no size restrictions and surpasses information theoretic limitations. The AF-heap belongs to the Fibonacci heap family.< >