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Relaxed weak queues: an alternative to runrelaxed heaps
, 2005
"... Abstract. A simplification of a runrelaxed heap, called a relaxed weak queue, is presented. This new priorityqueue implementation supports all operations as efficiently as the original: findmin, insert, and decrease (also called decreasekey) in O(1) worstcase time, and delete in O(lg n) worstc ..."
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Abstract. A simplification of a runrelaxed heap, called a relaxed weak queue, is presented. This new priorityqueue implementation supports all operations as efficiently as the original: findmin, insert, and decrease (also called decreasekey) in O(1) worstcase time, and delete in O(lg n) worstcase time, n denoting the number of elements stored prior to the operation. These time bounds are valid on a pointer machine as well as on a randomaccess machine. A relaxed weak queue is a collection of at most ⌊lg n ⌋ + 1 perfect weak heaps, where there are in total at most ⌊lg n ⌋ + 1 nodes that may violate weakheap order. In a pointerbased representation of a perfect weak heap, which is a binary tree, it is enough to use two pointers per node to record parentchild relationships. Due to decrease, each node must store one additional pointer. The auxiliary data structures maintained to keep track of perfect weak heaps and potential violation nodes only require O(lg n) words of storage. That is, excluding the space used by the elements themselves, the total space usage of a relaxed weak queue can be as low as 3n + O(lg n) words. ACM CCS Categories and Subject Descriptors. E.1 [Data Structures]: Lists, stacks, and queues; E.2 [Data Storage Representations]: Linked representations;
Early Grouping Gets The Skew
, 2002
"... We propose a new algorithm for external grouping with a large result set. Our approach handles skewed data gracefully and lowers the amount of random IO on disk considerably. ..."
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We propose a new algorithm for external grouping with a large result set. Our approach handles skewed data gracefully and lowers the amount of random IO on disk considerably.
RankRelaxed Weak Queues: Faster than Pairing and Fibonacci Heaps?
, 2009
"... A runrelaxed weak queue by Elmasry et al. (2005) is a priority queue data structure with insert and decreasekey in O(1) as well as delete and deletemin in O(log n) worstcase time. One further advantage is the small space consumption of 3n + O(log n) pointers. In this paper we propose rankrelaxe ..."
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A runrelaxed weak queue by Elmasry et al. (2005) is a priority queue data structure with insert and decreasekey in O(1) as well as delete and deletemin in O(log n) worstcase time. One further advantage is the small space consumption of 3n + O(log n) pointers. In this paper we propose rankrelaxed weak queues, reducing the number of rank violations nodes for each level to a constant, while providing amortized constant time for decreasekey. Compared to runrelaxed weak queues, the new structure additionally gains one pointer per node. An empirical evaluation shows that the implementation can outperform Fibonacci and pairing heaps in practice even on rather simple data types.
The WeakHeap Data Structure: Variants and Applications1
"... The weak heap is a priority queue that was introduced as a competitive structure for sorting. Its arraybased form supports the operations findmin in O(1) worstcase time, and insert and deletemin in O(lg n) worstcase time using at most dlg ne element comparisons. Additionally, its pointerbased ..."
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The weak heap is a priority queue that was introduced as a competitive structure for sorting. Its arraybased form supports the operations findmin in O(1) worstcase time, and insert and deletemin in O(lg n) worstcase time using at most dlg ne element comparisons. Additionally, its pointerbased form supports delete and decrease in O(lg n) worstcase time using at most dlg ne element comparisons. In this paper we enhance this data structure as follows: 1. We improve the arraybased form to support insert in O(1) amortized time. The main idea is to temporarily store the inserted elements in a buffer, and, once the buffer is full, to move its elements to the heap using an efficient bulkinsertion procedure. As an application, we use this variant in the implementation of adaptive heapsort. Accordingly, we guarantee, for several measures of disorder, that the formula expressing the number of element comparisons performed by the algorithm is optimal up to the constant factor of the highorder term. Unlike other previous constant
Heapsort using Multiple Heaps
"... We present a modification of the inplace algorithm HEAPSORT using multiple heaps. Our algorithm reduces the number of swaps made between the elements of the heap structure after the removal of the root at the cost of some extra comparisons. In order to retain the property of sorting inplace, we pe ..."
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We present a modification of the inplace algorithm HEAPSORT using multiple heaps. Our algorithm reduces the number of swaps made between the elements of the heap structure after the removal of the root at the cost of some extra comparisons. In order to retain the property of sorting inplace, we perform a kind of multiplexing and store all heaps in a single array such that no extra space is required. We also present a theoretical analysis of our algorithm, providing a specific formula for computing the optimal number of heaps to be used, and back up our theoretical findings with an experimental study, which shows the superiority of our approach with respect to the classical HEAPSORT. 1.
MKWI 2010 – Planung/Scheduling und Konfigurieren/Entwerfen 2295 Finding the Needle in the Haystack with Heuristically Guided Swarm Tree Search
"... Abstract. In this paper we consider the search in large state spaces with high branching factors and an objective function to be maximized. Our method portfolio, which we refer to as heuristically guided swarm tree search, is randomized, as it consists of several MonteCarlo runs, and guided, as it ..."
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Abstract. In this paper we consider the search in large state spaces with high branching factors and an objective function to be maximized. Our method portfolio, which we refer to as heuristically guided swarm tree search, is randomized, as it consists of several MonteCarlo runs, and guided, as it relies on fitness selection. We apply different search enhancement such as UCT, lookaheads, multiple runs, symmetry detection and parallel search to increase coverage and solution quality. Theoretically, we show that UCT, which trades exploration for exploitation, can be more successful on several runs than on only one. We look at two case studies. For the Same Game we devise efficient node evaluation functions and tabu color lists. For Morpion Solitaire the graph to be searched is reduced to a tree. We also adapt the search to the graphics processing unit. 1