## Abstract On the Power of Structural Violations in Priority Queues

Citations: | 1 - 0 self |

### BibTeX

@MISC{Elmasry_abstracton,

author = {Amr Elmasry and Claus Jensen and Jyrki Katajainen},

title = {Abstract On the Power of Structural Violations in Priority Queues},

year = {}

}

### OpenURL

### Abstract

We give a priority queue that guarantees the worstcase cost of Θ(1) per minimum finding, insertion, and decrease; and the worst-case cost of Θ(lg n) with at most lg n + O ( √ lg n) element comparisons per deletion. Here, n denotes the number of elements stored in the data structure prior to the operation in question, and lg n is a shorthand for max {1,log 2 n}. In contrast to a run-relaxed heap, which allows heaporder violations, our priority queue relies on structural violations. By mimicking a priority queue that allows heap-order violations with one that only allows structural violations, we improve the bound on the number of element comparisons per deletion to lg n + O(lg lg n).

### Citations

591 |
Fibonacci heaps and their uses in improved network optimization algorithms
- Fredman, Tarjan
- 1984
(Show Context)
Citation Context ...order violation means that a node stores an element that is smaller than the element stored at its parent. A separate structure is maintained to keep track of all such violations. In Fibonacci heaps (=-=Fredman & Tarjan 1987-=-) and thin heaps (Kaplan & Tarjan 1999) structural violations are allowed. A structural violation means that a node has lost one or more of its subtrees. Kaplan & Tarjan Partially supported by the Dan... |

87 |
Leiserson, Introduction to Algorithms, 2nd edn
- Cormen, Stein, et al.
- 2001
(Show Context)
Citation Context ... worst case at most two 2’s need to be fixed up per increment and decrement. 2.2 Pruned binomial queues A pruned binomial tree can be represented in the same way as a normal binomial tree [see, e.g. (=-=Cormen et al. 2001-=-)]; each node stores an element, a degree, a parent pointer, a child pointer, and two sibling pointers. To support the two-tier framework, the nodes should store yet another pointer to link a node in ... |

78 |
Relaxed heaps: an alternative to Fibonacci heaps with applications to parallel computation
- Driscoll, Gabow, et al.
- 1988
(Show Context)
Citation Context ...here Φ is the golden ratio. This bound can be reduced to log Φ n + O(lg lg n) using the twotier framework described in (Elmasry 2004, Elmasry et al. 2004) (log Φ n ≈ 1.44lg n). For run-relaxed heaps (=-=Driscoll et al. 1988-=-) this bound is 3lg n+O(1) in the worst case [as analysed in (Elmasry et al. 2004, Elmasry et al. 2006)], and the bound can be improved to lg n + O(lg lg n) using the two-tier framework (Elmasry et al... |

41 |
Implementation and analysis of binomial queue algorithms
- BROWN
- 1978
(Show Context)
Citation Context ...concerning priority queues, but refer to any textbook on data structures and algorithms [see, for instance, (Cormen, Leiserson, Rivest & Stein 2001)]. There are two ways of relaxing a binomial queue (=-=Brown 1978-=-, Vuillemin 1978) to support decrease at a cost of O(1). In run-relaxed heaps (Driscoll, Gabow, Shrairman & Tarjan 1988) heap-order violations are allowed. In a min-heap, a heap-order violation means ... |

21 | Worst-case optimal insertion and deletion methods for decomposable searching problems - Overmars, Leeuwen - 1981 |

18 |
Meldable heaps and Boolean union-find
- Kaplan, Shafrir, et al.
- 2002
(Show Context)
Citation Context ...as a counter representing a number in this redundant number system. To allow increments and decrements at any digit at constant cost, we use a regular counter discussed, for example, in (Brodal 1996, =-=Kaplan et al. 2002-=-). Following the guidelines given in (Elmasry 2004, Elmasry et al. 2004), our data structure has two main components, an upper store and a lower store, and both are implemented as pruned binomial queu... |

16 | Resizable arrays in optimal time and space - Brodnik, Carlsson, et al. - 1999 |

12 |
New heap data structures
- Kaplan, Tarjan
- 1999
(Show Context)
Citation Context ...s an element that is smaller than the element stored at its parent. A separate structure is maintained to keep track of all such violations. In Fibonacci heaps (Fredman & Tarjan 1987) and thin heaps (=-=Kaplan & Tarjan 1999-=-) structural violations are allowed. A structural violation means that a node has lost one or more of its subtrees. Kaplan & Tarjan Partially supported by the Danish Natural Science Research Council u... |

11 | Two-tier relaxed heaps
- Elmasry, Jensen, et al.
(Show Context)
Citation Context ...rk described in (Elmasry 2004, Elmasry et al. 2004) (log Φ n ≈ 1.44lg n). For run-relaxed heaps (Driscoll et al. 1988) this bound is 3lg n+O(1) in the worst case [as analysed in (Elmasry et al. 2004, =-=Elmasry et al. 2006-=-)], and the bound can be improved to lg n + O(lg lg n) using the two-tier framework (Elmasry et al. 2004, Elmasry et al. 2006). For fat heaps (Kaplan, Shafrir, & Tarjan 2002, Kaplan & Tarjan 1999) the... |

11 | Experiences with the design and implementation of space-efficient deques
- Katajainen, Mortensen
(Show Context)
Citation Context ... at the tail is possible at the worst-case cost of O(1), which is achievable, for example, by doubling, halving, and incremental copying [see also (Brodnik, Carlsson, Demaine, Munro & Sedgewick 1999, =-=Katajainen & Mortensen 2001-=-)]. We let each priority-queue operation maintain a pointer to the last entry in use and initiate reorganization whenever necessary. In our application, the ith entry of a guide stores a list of up to... |

8 | A framework for speeding up priorityqueue operations
- Elmasry, Jensen, et al.
- 2004
(Show Context)
Citation Context ...delete-min and delete is 2log Φ n + O(1) in the amortized sense, where Φ is the golden ratio. This bound can be reduced to log Φ n + O(lg lg n) using the twotier framework described in (Elmasry 2004, =-=Elmasry et al. 2004-=-) (log Φ n ≈ 1.44lg n). For run-relaxed heaps (Driscoll et al. 1988) this bound is 3lg n+O(1) in the worst case [as analysed in (Elmasry et al. 2004, Elmasry et al. 2006)], and the bound can be improv... |

6 | Layered heaps - Elmasry - 2004 |

1 | Bk−1 c Bk−1 z Bk d Bk s Bk−1 s Bk−1 c Bk−1 Bk−1 d Bk z Bk Brodal - S - 1996 |

1 | Layered heaps, in ‘Proceedings of the 9th Scandinavian Workshop on Algorithm Theory - Elmasry - 2004 |