Worst-case Analysis of Set Union Algorithms
Journal of the ACM (JACM)
Data structures and network algorithms
Data structures and network algorithms
Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Range-restricted mergeable priority queues
Information Processing Letters
Surpassing the information theoretic bound with fusion trees
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Trans-dichotomous algorithms for minimum spanning trees and shortest paths
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
A randomized linear-time algorithm to find minimum spanning trees
Journal of the ACM (JACM)
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
A minimum spanning tree algorithm with inverse-Ackermann type complexity
Journal of the ACM (JACM)
An optimal minimum spanning tree algorithm
Journal of the ACM (JACM)
Meldable heaps and boolean union-find
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Deterministic sorting in O(nlog log n) time and linear space
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Introduction to Algorithms
On AC0 implementations of fusion trees and atomic heaps
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Integer Sorting in 0(n sqrt (log log n)) Expected Time and Linear Space
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Equivalence between Priority Queues and Sorting
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Meldable RAM priority queues and minimum directed spanning trees
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Black box for constant-time insertion in priority queues (note)
ACM Transactions on Algorithms (TALG)
Union-find with constant time deletions
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Equivalence between priority queues and sorting
Journal of the ACM (JACM)
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We show that any priority queue data structure that supports insert, delete, and find-min operations in pq(n) amortized time, where n is an upper bound on the number of elements in the priority queue, can be converted into a priority queue data structure that also supports fast meld operations with essentially no increase in the amortized cost of the other operations. More specifically, the new data structure supports insert, meld and find-min operations in O(1) amortized time, and delete operations in O(pq(n) + α(n)) amortized time, where α(n) is a functional inverse of the Ackermann function, and where n this time is the total number of operations performed on all the priority queues. The construction is very simple. The meldable priority queues are obtained by placing a nonmeldable priority queues at each node of a union-find data structure. We also show that when all keys are integers in the range [1, N], we can replace n in the bound stated previously by min{n, N}.Applying this result to the nonmeldable priority queue data structures obtained recently by Thorup [2002b] and by Han and Thorup [2002] we obtain meldable RAM priority queues with O(log log n) amortized time per operation, or O(&sqrt;log log n) expected amortized time per operation, respectively. As a by-product, we obtain improved algorithms for the minimum directed spanning tree problem on graphs with integer edge weights, namely, a deterministic O(m log log n)-time algorithm and a randomized O(m&sqrt;log log n)-time algorithm. For sparse enough graphs, these bounds improve on the O(m + n log n) running time of an algorithm by Gabow et al. [1986] that works for arbitrary edge weights.