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A Parallel Priority Queue with Constant Time Operations
 JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING
, 1998
"... We present a parallel priority queue that supports the following operations in constant time: parallel insertion of a sequence of elements ordered according to key, parallel decrease key for a sequence of elements ordered according to key, deletion of the minimum key element, as well as deletion ..."
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Cited by 15 (1 self)
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We present a parallel priority queue that supports the following operations in constant time: parallel insertion of a sequence of elements ordered according to key, parallel decrease key for a sequence of elements ordered according to key, deletion of the minimum key element, as well as deletion of an arbitrary element. Our data structure is the first to support multi insertion and multi decrease key in constant time. The priority queue can be implemented on the EREW PRAM, and can perform any sequence of n operations in O(n) time and O(m log n) work, m being the total number of keys inserted and/or updated. A main application is a parallel implementation of Dijkstra's algorithm for the singlesource shortest path problem, which runs in O(n) time and O(m log n) work on a CREW PRAM on graphs with n vertices and m edges. This is a logarithmic factor improvement in the running time compared with previous approaches.
Purely Functional, RealTime Deques with Catenation
 Journal of the ACM
, 1999
"... We describe an efficient, purely functional implementation of deques with catenation. In addition to being an intriguing problem in its own right, finding a purely functional implementation of catenable deques is required to add certain sophisticated programming constructs to functional programming ..."
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Cited by 13 (2 self)
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We describe an efficient, purely functional implementation of deques with catenation. In addition to being an intriguing problem in its own right, finding a purely functional implementation of catenable deques is required to add certain sophisticated programming constructs to functional programming languages. Our solution has a worstcase running time of O(1) for each push, pop, inject, eject and catenation. The best previously known solution has an O(log k) time bound for the k deque operation. Our solution is not only faster but simpler. A key idea used in our result is an algorithmic technique related to the redundant digital representations used to avoid carry propagation in binary counting.
Twotier relaxed heaps
 Proceedings of the 17th International Symposium on Algorithms and Computation, Lecture Notes in Computer Science 4288, SpringerVerlag
, 2006
"... Abstract. We introduce an adaptation of runrelaxed heaps which provides efficient heap operations with respect to the number of element comparisons performed. Our data structure guarantees the worstcase cost of O(1) for findmin, insert, and decrease; and the worstcase cost of O(lg n) with at mos ..."
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Cited by 11 (8 self)
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Abstract. We introduce an adaptation of runrelaxed heaps which provides efficient heap operations with respect to the number of element comparisons performed. Our data structure guarantees the worstcase cost of O(1) for findmin, insert, and decrease; and the worstcase cost of O(lg n) with at most lg n + 3 lg lg n + O(1) element comparisons for delete, improving the bound of 3lg n + O(1) on the number of element comparisons known for runrelaxed heaps. Here, n denotes the number of elements stored prior to the operation in question, and lg n equals max {1, log 2 n}. 1
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
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 ..."
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Cited by 5 (5 self)
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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.
Buckets, Heaps, Lists, and Monotone Priority Queues
, 1997
"... We introduce the heapontop (hot) priority queue data structure that combines the multilevel bucket data structure of Denardo and Fox and a heap. We use the new data structure to obtain an O(m + n(log C) 1 3 +ffl ) expected time implementation of Dijkstra's shortest path algorithm, improving the ..."
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Cited by 4 (0 self)
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We introduce the heapontop (hot) priority queue data structure that combines the multilevel bucket data structure of Denardo and Fox and a heap. We use the new data structure to obtain an O(m + n(log C) 1 3 +ffl ) expected time implementation of Dijkstra's shortest path algorithm, improving the previous bounds. We can implement hot queues even more efficiently in practice by using sorted lists to represent small priority queues. Our experimental results in the context of Dijkstra's algorithm show that this implementation of hot queues performs very well and is more robust than implementations based only on heap or multilevel bucket data structures. 1 Introduction A priority queue is a data structure that maintains a set of elements and supports operations insert, decreasekey, and extractmin. Priority queues are fundamental data structures with many applications. Typical applications include graph algorithms (e.g. [14]) and event simulation (e.g. [5]). An important subclass of...
HeaponTop Priority Queues
 TR 96042, NEC RESEARCH INSTITUTE
, 1996
"... We introduce the heapontop (hot) priority queue data structure that combines the multilevel bucket data structure of Denardo and Fox [9] and a heap. We use the new data structure to obtain an O(m+n(logC) 1 3 +ffl ) expected time implementation of Dijkstra's shortest path algorithm [11], improvi ..."
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Cited by 4 (2 self)
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We introduce the heapontop (hot) priority queue data structure that combines the multilevel bucket data structure of Denardo and Fox [9] and a heap. We use the new data structure to obtain an O(m+n(logC) 1 3 +ffl ) expected time implementation of Dijkstra's shortest path algorithm [11], improving the previous bounds.
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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Cited by 4 (3 self)
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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;
A Note on Worst Case Efficient Meldable Priority Queues
, 1996
"... We give a simple implementation of meldable priority queues, achieving Insert , Find min, and Meld in O(1) worst case time, and Delete min and Delete in O(log n) worst case time. 1 Introduction The implementation of priority queues is a classic problem in computer science. The fundamental operatio ..."
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Cited by 3 (0 self)
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We give a simple implementation of meldable priority queues, achieving Insert , Find min, and Meld in O(1) worst case time, and Delete min and Delete in O(log n) worst case time. 1 Introduction The implementation of priority queues is a classic problem in computer science. The fundamental operations are Insert and Delete min, but various extra operations, such as Find min, Meld, Delete, and Decrease key , have been considered. Fibonacci heaps [6] support all of these, in O(log n) time for the Delete min and Delete operations, and O(1) for the rest. These bounds are, however, only amortized. Some earlier proposals [4, 5, 8] achieve such bounds in the 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 opera...
Project proposal: A meldable, iteratorvalid priority queue, CPH
, 2005
"... Abstract. The Standard Template Library (STL) is a library of generic algorithms and data structures that has been incorporated in the C++ standard and ships with all modern C++ compilers. In the CPH STL project the goal is to implement an enhanced edition of the STL. The priorityqueue class of the ..."
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Cited by 2 (2 self)
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Abstract. The Standard Template Library (STL) is a library of generic algorithms and data structures that has been incorporated in the C++ standard and ships with all modern C++ compilers. In the CPH STL project the goal is to implement an enhanced edition of the STL. The priorityqueue class of the STL is just an adapter that makes any resizable array to a queue in which the elements stored are arranged according to a given ordering function. In the C++ standard no compulsory support for the operations delete(), increase(), or meld() is demanded even if those are utilized in many algorithms solving graphtheoretic or geometric problems. In this project, the goal is to implement a CPH STL extension of the priorityqueue class which provides, in addition to the normal priorityqueue functionality, the operations delete(), increase(), and meld(). To make the first two of these operations possible, the class must also guarantee that external references to compartments inside the data structure are kept valid at all times.