G. S. Brodal. Worst-case efficient priority queues. In Proc. 7th ACM-SIAM Symposium on Discrete Algorithms, pages 52--58, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....in which numbers have more than one representation and a single digit change is all that is needed to add one. Clancy and Knuth [9] used this idea in an implementation of finger search trees. Descriptions of such redundant representations as well as other applications can be found in [2, 9, 28]. The Clancy Knuth method represents numbers in base two but using three digits, 0,1, and 2. A redundant binary representation (RBR) of a non negative number x is a sequence of digits d n , d n Gamma1 , d 0 with d i 2 f0; 1; 2g and x = P n i=0 d i 2 . Such a representation is in ....

G. S. Brodal. Worst-case efficient priority queues. In Proc. 7th ACM-SIAM Symposium on Discrete Algorithms, pages 52--58, 1996.

....In existing priority queue implementations the approach is two fold. Most data structures require storing additional balance information associated with queue nodes in order to guarantee the worst case efficiency of individual operations (e.g. leftist trees [8] relaxed heaps [5] Brodal queues [3, 4]) Others achieve good amortized performance by adjusting the structure during some operations rather than struggling to maintain balance constantly (skew heaps [12, 13] pairing heaps [6] Experiments indicate that the latter approach is more promising in practice [1, 7, 9] This is due to the ....

G. S. Brodal, Worst-case efficient Priority Queues, Proc. 17th ACM-SIAM Symposium on Discrete Algorithms, 1996, 52-58.

....most recent element extracted from the queue. In this paper we deal with monotone priority queues. Unless mentioned otherwise, we refer to priority queues whose operation time bounds depend only on the number of elements on the queue as heaps. The fastest implementations of heaps are described in [3, 10, 12]. Alternative implementations of priority queues use buckets (e.g. 1, 5, 7, 8] Operation times for bucket based implementations depend on the maximum event duration C, defined in Section 2. See [2] for a related data structure. Heaps are particularly efficient when the number of elements on the ....

G. S. Brodal. Worst-Case Efficient Priority Queues. In Proc. 7th ACMSIAM Symposium on Discrete Algorithms, pages 52--58, 1996.

....In existing priority queue implementations the approach is two fold. Most data structures require storing additional balance information associated with queue nodes in order to guarantee the worst case efficiency of individual operations (e.g. leftist trees [8] relaxed heaps [5] Brodal queues [3, 4]) Others achieve good amortized performance by adjusting the structure during some operations rather than struggling to maintain balance constantly (skew heaps [12, 13] pairing heaps [6] Experiments indicate that the latter approach is more promising in practice [1, 7, 9] This is due to the ....

G. S. Brodal, Worst-case efficient Priority Queues, Proc. 17th ACM-SIAM Symposium on Discrete Algorithms, 1996, 52-58.

....most recent element extracted from the queue. In this paper we deal with monotone priority queues. Unless mentioned otherwise, we refer to priority queues whose operation time bounds depend only on the number of elements on the queue as heaps. The fastest implementations of heaps are described in [4, 14, 19]. Alternative implementations of priority queues use buckets (e.g. 2, 7, 11, 12] Operation times for bucketbased implementations depend on the maximum event duration C, defined in Section 2. See [3] for a related data structure. Heaps are particularly efficient when the number of elements on ....

G. S. Brodal. Worst-Case Efficient Priority Queues. In Proc. 7th ACM-SIAM Symposium on Discrete Algorithms, pages 52--58, 1996.

....the latest element extracted from the queue. In this paper we deal with monotone priority queues. Unless mentioned otherwise, we refer to priority queues whose operation time bounds depend only on the number of elements on the queue as heaps. The fastest implementations of heaps are described in [4, 12, 15]. Alternative implementations of priority queues use buckets (e.g. 2, 6, 9, 10] Operation times for bucket based implementations depend on the maximum event duration C, defined in Section 2. See [3] for a related data structure. Heaps are more efficient when the number of elements on the heap ....

G. S. Brodal. Worst-Case Efficient Priority Queues. In Proc. 7th ACM-SIAM Symposium on Discrete Algorithms, pages 52--58, 1996.

....queue is small as s heaps. 1 For example, in a binary heap containing n elements, all priority queue operations take O(n) time, so the binary heap is an s heap. Operation bounds may depend on parameters other than the number of elements. The fastest implementations of s heaps are described in [4, 12, 17]. Alternative implementations of priority queues use buckets (e.g. 2, 7, 9, 10] Operation times for bucket based implementations depend on the maximum event duration C, defined in Section 2, and are not very sensitive to the number of elements. See [3] for a related data structure. s heaps are ....

G. S. Brodal. Worst-Case Efficient Priority Queues. In Proc. 7th ACM-SIAM Symposium on Discrete Algorithms, pages 52--58, 1996.

....shortest path problem has efficient sequential solutions, especially when G has nonnegative edge weights. In this case, the problem can be solved by Dijkstra s algorithm in O(m n log n) time using the Fibonacci heap or another priority queue data structure with the same resource bounds [2, 4, 6]. If in addition G is planar, then the problem can be solved optimally in O(n) time [11] In this paper we consider the single source shortest path problem in planar digraphs with nonnegative real edge weights. Despite much effort, no sublinear time, work optimal parallel algorithm has been ....

....parallel Dijkstra, is straightforward, and obtained by doing distance label updates in parallel. The idea is as follows. Let each of the p processors have a private heap supporting insert and decrease key operations in constant time, and find and delete min in O(log n) time, all in worst case [2, 4]. Assume that a vertex of minimum tentative distance has been selected and broadcast to the p processors before the start of the next iteration. The adjacency list of the selected vertex is divided into p equal sized segments, such that the distance labels of the adjacent vertices can be updated ....

Gerth Stølting Brodal. Worst-case efficient priority queues. In Proc. 7th ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 52--58, 1996.

....worst case sense for various subsets of the operations supported by Fibonacci heaps. None of these subsets includes the meld operation. This has been remedied recently by Brodal, who has given worst case solutions, first [2] for the set Insert, Delete min, Find min, Meld, and Delete, and later [3] for the full set of Fibonacci heap operations. The latter result has been achieved independently by Boyapati and Rangan [1] By the lower bound on sorting, no strictly better set of complexities can be found in the comparison model. The recent solutions for worst case efficient meldable priority ....

....The latter result has been achieved independently by Boyapati and Rangan [1] By the lower bound on sorting, no strictly better set of complexities can be found in the comparison model. The recent solutions for worst case efficient meldable priority queues are quite involved, in particular [1, 3], but even in [2] each element needs four pointers and two information fields, and the code for the operations contains many cases. Our purpose here is to present an alternative way of implementing a priority queue achieving the bounds in [2] Our structure uses only E mail address: ....

Gerth S. Brodal. Worst-case efficient priority queues. In Proc. 7th SODA, pages 52--58, 1996.

....Nordic Journal of Computing, Selected Papers of the 5th Scandinavian Workshop on Algorithm Theory (SWAT 96) volume 3(4) pages 337 351, 1996. Chapter 5 [15] Fast Meldable Priority Queues. In Proc. 4th Workshop on Algorithms and Data Structures, LNCS volume 955, pages 282 290, 1995. Chapter 6 [18]: Worst Case Efficient Priority Queues. In Proc. 7th ACM SIAM Symposium on Discrete Algorithms, pages 52 58, 1996. Chapter 7 [17] Priority Queues on Parallel Machines. In Proc. 5th Scandinavian Workshop on Algorithm Theory, LNCS volume 1097, pages 416 427, 1996. Chapter 8 [23] A Parallel ....

....operations MakeQueue, Insert, Meld, FindMin, DeleteMin, Delete and DecreaseKey in constant time. Category: E.1, F.1.2 Keywords: priority queues, meld, PRAM, worst case complexity 7.1 Introduction The construction of priority queues is a classical topic in data structures. Some references are [15, 18, 43, 49, 52, 53, 108, 109]. A historical overview of implementations can be found in [76] Recently several papers have also considered how to implement priority queues on parallel machines [28, 32, 35, 70, 89, 90, 94, 95] In this paper we focus on how to achieve optimal speedup for the individual priority queue ....

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Gerth Stølting Brodal. Worst-case efficient priority queues. In Proc. 7th ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 52--58, 1996.

.... operations by using efficient priority queues like Fibonacci heaps [12] for maintaining tentative distances, or other priority queue implementations supporting deletion of the minimum key element in amortized or worst case logarithmic time, and decrease key in amortized or worst case constant time [3, 11, 17]. The single source shortest path problem is in NC (by virtue of the all pairs shortest path problem being in NC) and thus a fast parallel algorithm exists, but for general digraphs no work efficient algorithm in NC is known. The best NC algorithm runs in O(log 2 n) time and performs O(n 3 ....

Gerth Stølting Brodal. Worst-case efficient priority queues. In Proc. 7th ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 52--58, 1996.

.... operations by using efficient priority queues like Fibonacci heaps [7] for maintaining tentative distances, or other priority queue implementations supporting deletion of the minimum key element in amortized or worst case logarithmic time, and decrease key in amortized or worst case constant time [3, 6, 10]. The single source shortest path problem is in NC (by virtue of the all pairs shortest path problem being in NC) and thus a fast parallel algorithm exists, but for general digraphs no work efficient algorithm in NC is known. The best NC algorithm runs in O(log 2 n) time and performs O(n 3 ....

G. Brodal. Worst-case efficient priority queues. In Proc. 7th ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 52--58, 1996.

.... operations by using efficient priority queues like Fibonacci heaps [13] for maintaining tentative distances, or other priority queue implementations supporting deletion of the minimum key element in amortized or worst case logarithmic time, and decrease key in amortized or worst case constant time [3, 12, 18]. The single source shortest path problem is in NC (by virtue of the all pairs shortest path problem being in NC) and thus a fast parallel algorithm exists, but for general digraphs no work efficient algorithm in NC is known. The best NC algorithm runs in O(log 2 n) time and performs O(n 3 ....

G. S. Brodal. Worst-case efficient priority queues. In Proc. 7th ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 52--58, 1996.

....of the priority queues adopt to a processor array of size O(log n) supporting the operations MakeQueue, Insert, Meld, FindMin, ExtractMin, Delete and DecreaseKey in constant time. 1 Introduction The construction of priority queues is a classical topic in data structures. Some references are [1, 2, 6, 7, 8, 9, 19, 20]. A historical overview of implementations can be found in [13] Recently several papers have also considered how to implement priority queues on parallel machines [3, 4, 5, 11, 15, 16, 17, 18] In this paper we focus on how to achieve optimal speedup for the individual priority queue operations ....

Gerth Stølting Brodal. Worst-case efficient priority queues. In Proc. 7th ACMSIAM Symposium on Discrete Algorithms (SODA), pages 52--58, 1996.

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