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Replacing mark bits with randomness in Fibonacci heaps
, 2014
"... A Fibonacci heap is a deterministic data structure implementing a priority queue with optimal amortized asymptotic operation costs. An unaesthetic aspect of Fibonacci heaps is that they must maintain a “mark bit ” which serves only to ensure efficiency of heap operations, not their correctness. Kar ..."
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. Karger proposed a simple randomized variant of Fibonacci heaps in which mark bits are replaced by coin flips. This modified data structure still has expected amortized cost O(1) for insert, decreasekey, and merge. Karger conjectured that this data structure has expected amortized cost O(log s
Thin Heaps, Thick Heaps
, 2006
"... The Fibonacci heap was devised to provide an especially efficient implementation of Dijkstra’s shortest path algorithm. Although asyptotically efficient, it is not as fast in practice as other heap implementations. Expanding on ideas of Høyer, we describe three heap implementations (two versions of ..."
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Cited by 9 (5 self)
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The Fibonacci heap was devised to provide an especially efficient implementation of Dijkstra’s shortest path algorithm. Although asyptotically efficient, it is not as fast in practice as other heap implementations. Expanding on ideas of Høyer, we describe three heap implementations (two versions
Fibonacci heaps revisited
 CoRR
"... The Fibonacci heap is a classic data structure that supports deletions in logarithmic amortized time and all other heap operations in O(1) amortized time. We explore the design space of this data structure. We propose a version with the following improvements over the original: (i) Each heap is repr ..."
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Cited by 1 (1 self)
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The Fibonacci heap is a classic data structure that supports deletions in logarithmic amortized time and all other heap operations in O(1) amortized time. We explore the design space of this data structure. We propose a version with the following improvements over the original: (i) Each heap
Violation heaps: A better substitute for Fibonacci heaps
, 2008
"... We give a priority queue that achieves the same amortized bounds as Fibonacci heaps. Namely, findmin requires O(1) worstcase time, insert, meld and decreasekey require O(1) amortized time, and deletemin requires O(log n) amortized time. Our structure is simple and promises a more efficient pract ..."
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Cited by 3 (0 self)
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We give a priority queue that achieves the same amortized bounds as Fibonacci heaps. Namely, findmin requires O(1) worstcase time, insert, meld and decreasekey require O(1) amortized time, and deletemin requires O(log n) amortized time. Our structure is simple and promises a more efficient
Are Fibonacci Heaps Optimal?
 ISAAC'94, LNCS
, 1994
"... In this paper we investigate the inherent complexity of the priority queue abstract data type. We show that, under reasonable assumptions, there exist sequences of n Insert, n Delete, m DecreaseKey and t FindMin operations, where 1 t n, which have W(nlogt + n + m) complexity. Although Fibonacci h ..."
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Cited by 7 (0 self)
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heaps do not achieve this bound, we present a modified Fibonacci heap which does, and so is optimal under our assumptions.
Strict Fibonacci Heaps
 STOC
, 2012
"... We present the first pointerbased heap implementation with time bounds matching those of Fibonacci heaps in the worst case. We support makeheap, insert, findmin, meld and decreasekey in worstcase O(1) time, and delete and deletemin in worstcase O(lgn) time, where n is the size of the heap. The ..."
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Cited by 5 (3 self)
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We present the first pointerbased heap implementation with time bounds matching those of Fibonacci heaps in the worst case. We support makeheap, insert, findmin, meld and decreasekey in worstcase O(1) time, and delete and deletemin in worstcase O(lgn) time, where n is the size of the heap
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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Cited by 1 (1 self)
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outperform Fibonacci and pairing heaps in practice even on rather simple data types.
Hollow Heaps
"... We introduce the hollow heap, a very simple data structure with the same amortized efficiency as the classical Fibonacci heap. All heap operations except delete and deletemin take O(1) time, worst case as well as amortized; delete and deletemin take O(log n) amortized time. Hollow heaps are by far ..."
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We introduce the hollow heap, a very simple data structure with the same amortized efficiency as the classical Fibonacci heap. All heap operations except delete and deletemin take O(1) time, worst case as well as amortized; delete and deletemin take O(log n) amortized time. Hollow heaps
Relaxed Fibonacci heaps: An alternative to Fibonacci heaps with worst case rather than amortized time bounds
, 1995
"... We present a new data structure called relaxed Fibonacci heaps for implementing priority queues on a RAM. Relaxed Fibonacci heaps support the operations nd minimum, insert, decrease key and meld, each in O(1) worst case time and delete and delete min in O(log n) worst case time. ..."
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We present a new data structure called relaxed Fibonacci heaps for implementing priority queues on a RAM. Relaxed Fibonacci heaps support the operations nd minimum, insert, decrease key and meld, each in O(1) worst case time and delete and delete min in O(log n) worst case time.
Heaps Simplified
"... Abstract. The heap is a basic data structure used in a wide variety of applications, including shortest path and minimum spanning tree algorithms. In this paper we explore the design space of comparisonbased, amortizedefficient heap implementations. From a consideration of dynamic singleeliminati ..."
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to support key decrease operations, obtaining the rankpairing heap, or rpheap. Rankpairing heaps combine the performance guarantees of Fibonacci heaps with simplicity approaching that of pairing heaps. Like pairing heaps, rankpairing heaps consist of trees of arbitrary structure, but these trees
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