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Two new methods for transforming priority queues into doubleended priority queues
 CPH STL Report
, 2006
"... Abstract. Two new ways of transforming a priority queue into a doubleended priority queue are introduced. These methods can be used to improve all known bounds for the comparison complexity of doubleended priorityqueue operations. Using an efficient priority queue, the first transformation can pr ..."
Abstract

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Abstract. Two new ways of transforming a priority queue into a doubleended priority queue are introduced. These methods can be used to improve all known bounds for the comparison complexity of doubleended priorityqueue operations. Using an efficient priority queue, the first transformation can produce a doubleended priority queue which guarantees the worstcase cost of O(1) for findmin, findmax, and insert; and the worstcase cost of O(lg n) including at most lg n + O(1) element comparisons for delete, but the data structure cannot support meld efficiently. Using a meldable priority queue that supports decrease efficiently, the second transformation can produce a meldable doubleended priority queue which guarantees the worstcase cost of O(1) for findmin, findmax, and insert; the worstcase cost of O(lg n) including at most lg n + O(lg lg n) element comparisons for delete; and the worstcase cost of O(min {lg m, lg n}) for meld. Here, m and n denote the number of elements stored in the data structures prior to the operation in question, and lg n is a shorthand for log 2 (max {2, n}). 1.
Probabilistic Data Structures for Priority Queues (Extended Abstract)
"... Abstract. We present several simple probabilistic data structures for implementing priority queues. We present a data structure called simple bottomup sampled heap (SBSH), supporting insert in O(1) expected time and delete, delete minimum, decrease key and meld in O(log n) time with high probabilit ..."
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Abstract. We present several simple probabilistic data structures for implementing priority queues. We present a data structure called simple bottomup sampled heap (SBSH), supporting insert in O(1) expected time and delete, delete minimum, decrease key and meld in O(log n) time with high probability. An extension of SBSH called BSH1, supporting insertandmeldinO(1) worst case time is presented. This data structure uses a novel “buffering technique ” to improve the expected bounds to worstcase bounds. Another extension of SBSH called BSH2, performing insert, decrease key and meld in O(1) amortized expected time and delete and delete minimum in O(log n) time with high probability is also presented. The amortized performance of this data structure is comparable to that of Fibonacci heaps (in probabilistic terms). Moreover, unlike Fibonacci heaps, each operation takes O(log n) time with high probability, making the data structure suitable for realtime applications.