Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Relaxed heaps: an alternative to Fibonacci heaps with applications to parallel computation
Communications of the ACM
Worst-case efficient priority queues
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
A data structure for manipulating priority queues
Communications of the ACM
Meldable heaps and boolean union-find
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Introduction to Algorithms
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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We give a priority queue that guarantees the worst-case cost of Θ(1) per minimum finding, insertion, and decrease; and the worst-case cost of Θ(lg n) with at most lg n + O(√lg n) element comparisons per deletion. Here, n denotes the number of elements stored in the data structure prior to the operation in question, and lg n is a shorthand for max {1, log2 n}. In contrast to a run-relaxed heap, which allows heap-order violations, our priority queue relies on structural violations. By mimicking a priority queue that allows heap-order violations with one that only allows structural violations, we improve the bound on the number of element comparisons per deletion to lg n + O(lg lg n).