An Optimal Minimum Spanning Tree Algorithm
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
ICDCN'06 Proceedings of the 8th international conference on Distributed Computing and Networking
Research paper: The saga of minimum spanning trees
Computer Science Review
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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.