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Very Fast Optimal Parallel Algorithms for Heap Construction
, 1994
"... We give two algorithms for permuting n items in an array into heap order on a CRCW PRAM. The first is deterministic and runs in O(log log n) time and performs O(n) operations. This runtime is the best possible for any comparisonbased algorithm using n processors. The second is randomized and runs ..."
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We give two algorithms for permuting n items in an array into heap order on a CRCW PRAM. The first is deterministic and runs in O(log log n) time and performs O(n) operations. This runtime is the best possible for any comparisonbased algorithm using n processors. The second is randomized and runs in O(log log log n) time with high probability, performing O(n) operations. No PRAM algorithm with o(log n) runtime was previously known for this problem. In order to obtain the deterministic result we study the parallel complexity of selecting the kth smallest of n elements on the CRCW PRAM, a problem that is of independent interest. We give an algorithm that is superior to existing ones when k is small compared to n. Consequently, we show that this problem can be solved in O(log log n + log k= log log n) time and O(n) operations for all 1 k n=2. A matching time lower bound is shown for all algorithms that use n or fewer processors to solve this problem. 1 Introduction A heap is a co...
On the Pending Event Set and Binary Tournaments
"... this paper we study the performance of the very first tournament based complete binary tree. We focus on discreteevent simulation and our results show that this unknown predecessor of heaps can be a more efficient alternative to the fastest pending event set implementations reported in the literatu ..."
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this paper we study the performance of the very first tournament based complete binary tree. We focus on discreteevent simulation and our results show that this unknown predecessor of heaps can be a more efficient alternative to the fastest pending event set implementations reported in the literature. We also extend the idea of binary tournaments to a (2; L)tournament structure which exhibits the property of delaying the processing of events with larger timestamps whilst it keeps similar theoretical performance bounds to the native (2; 1)structure or CBT. This property can be certainly useful in systems where many pending events are expected to be deleted or rescheduled during the simulation. 2 Tournament trees
Binary Tournaments and Priority Queues: PRAM and BSP
, 1997
"... We use an old idea of tournament based complete binary tree (CBT) to implement parallel priority queues (PQs). We show that this data structure enables a more efficient implementation of the operations extractmin and insert in terms of communications and synchronizations among processors than simil ..."
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We use an old idea of tournament based complete binary tree (CBT) to implement parallel priority queues (PQs). We show that this data structure enables a more efficient implementation of the operations extractmin and insert in terms of communications and synchronizations among processors than similar operations on the implicit heap. In most cases we only improve the asymptotic bounds on constant factors. However, some operations can be twice faster using simpler parallel algorithms upon the CBT. 1 Data structure and basic operations Every item stored in the PQ consists of a priority value and an indentifier. We associate every leaf of the CBT with one item, and use the internal nodes to maintain a continuous binary tournament among the items. A match, at internal node n, consists of determining the item with greater priority (less numerical value) between the two children of n and writing the identifier of the winner in n. The tournament is made up of a set of matches played in ever...
DiscreteEvent Simulation on the BulkSynchronous Parallel Model
, 1998
"... The bulksynchronous parallel (BSP) model of computing has been proposed to enable the development of portable software which achieves scalable performance across diverse parallel architectures. A number of applications of computing science have been demonstrated to be efficiently supported by the B ..."
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The bulksynchronous parallel (BSP) model of computing has been proposed to enable the development of portable software which achieves scalable performance across diverse parallel architectures. A number of applications of computing science have been demonstrated to be efficiently supported by the BSP model in practice.
Priority Queue Operations On EREWPRAM
, 1997
"... . Using EREWPRAM algorithms on a tournament based complete binary tree we implement the insert and extractmin operations with p = log N processors at costs O(1) and O(log log N) respectively. Previous solutions [4, 7] under the PRAM model and identical assumptions attain O(log log N) cost for both ..."
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. Using EREWPRAM algorithms on a tournament based complete binary tree we implement the insert and extractmin operations with p = log N processors at costs O(1) and O(log log N) respectively. Previous solutions [4, 7] under the PRAM model and identical assumptions attain O(log log N) cost for both operations. We also improve on constant factors the asymptotic bound for extractmin since in it we reduce the use of communication demanding primitives. The tournament tree enables the design of parallel algorithms that are noticeably simple. 1 Tournament trees Our data structure is a complete binary tree (CBT). Every item stored in the tree consists of a priority value and an identifier. We associate every leaf of the CBT with one item, and use the internal nodes to maintain a continuous binary tournament among the items. A match, at internal node n, consists of determining the item with higher priority (lesser numerical value) between the two children of n and writing the identifier of ...