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A framework for speeding up priorityqueue operations
, 2004
"... Abstract. We introduce a framework for reducing the number of element comparisons performed in priorityqueue operations. In particular, we give a priority queue which guarantees the worstcase cost of O(1) per minimum finding and insertion, and the worstcase cost of O(log n) with at most log n + O ..."
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Cited by 8 (8 self)
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Abstract. We introduce a framework for reducing the number of element comparisons performed in priorityqueue operations. In particular, we give a priority queue which guarantees the worstcase cost of O(1) per minimum finding and insertion, and the worstcase cost of O(log n) with at most log n + O(1) element comparisons per minimum deletion and deletion, improving the bound of 2log n + O(1) on the number of element comparisons known for binomial queues. Here, n denotes the number of elements stored in the data structure prior to the operation in question, and log n equals max {1,log 2 n}. We also give a priority queue that provides, in addition to the abovementioned methods, the prioritydecrease (or decreasekey) method. This priority queue achieves the worstcase cost of O(1) per minimum finding, insertion, and priority decrease; and the worstcase cost of O(log n) with at most log n + O(log log n) element comparisons per minimum deletion and deletion. CR Classification. E.1 [Data Structures]: Lists, stacks, and queues; E.2 [Data
On adaptive integer sorting
 In 12th Annual European Symposium on Algorithms, ESA 2004
, 2004
"... Abstract. This paper considers integer sorting on a RAM. We show that adaptive sorting of a sequence with qn inversions is asymptotically equivalent to multisorting groups of at most q keys, and a total of n keys. Using the recent O(n √ log log n) expected time sorting of Han and Thorup on each set, ..."
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Cited by 4 (0 self)
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Abstract. This paper considers integer sorting on a RAM. We show that adaptive sorting of a sequence with qn inversions is asymptotically equivalent to multisorting groups of at most q keys, and a total of n keys. Using the recent O(n √ log log n) expected time sorting of Han and Thorup on each set, we immediately get an adaptive expected sorting time of O(n √ log log q). Interestingly, for any positive constant ε, we show that multisorting and adaptive inversion sorting can be performed in (log n)1−ε linear time if q ≤ 2. We also show how to asymptotically improve the running time of any traditional sorting algorithm on a class of inputs much broader than those with few inversions. 1
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"... We study the performance of the most practical inversionsensitive internal sorting algorithms. Experimental results illustrate that adaptive AVL sort consumes the fewest number of comparisons unless the number of inversions is less than 1%; in such case Splaysort consumes the fewest number of compa ..."
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We study the performance of the most practical inversionsensitive internal sorting algorithms. Experimental results illustrate that adaptive AVL sort consumes the fewest number of comparisons unless the number of inversions is less than 1%; in such case Splaysort consumes the fewest number of comparisons. On the other hand, the running time of Quicksort is superior unless the number of inversions is less than 1.5%; in such case Splaysort has the shortest running time. Another interesting result is that although the number of cache misses for the cacheoptimal Greedysort algorithm was the least, compared to other adaptive sorting algorithms under investigation, it was outperformed by Quicksort.