## Optimal stable merging (1995)

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### Other Repositories/Bibliography

Venue: | The Computer Journal |

Citations: | 13 - 1 self |

### BibTeX

@ARTICLE{Symvonis95optimalstable,

author = {A Ntonios Symvonis},

title = {Optimal stable merging},

journal = {The Computer Journal},

year = {1995},

volume = {38},

pages = {681--690}

}

### OpenURL

### Abstract

### Citations

44 | A simple algorithm for merging two disjoint linearly ordered sets
- Hwang, Lin
- 1972
(Show Context)
Citation Context ...thm of Mannila O�m� and Ukkonen matches all the lower bounds (number of comparisons/ assignments and extra space) but is unstable. To achieve that, it uses the binary merge algorithm of Hwang and Lin =-=[18]-=-. This paper serves two purposes. First it presents a collection of useful techniques used in merging and, second, it presents an optimal stable in-place merging algorithm. We show how to make stable ... |

19 |
Practical in-place merging
- Huang, Langston
- 1988
(Show Context)
Citation Context ...ful enough to stabilize all of the unstable in-place merging algorithms known to the author. They are used to make stable the algorithms of Kronrod [3], Dvorak and Durian [13], and Huang and Langston =-=[15]-=-, as well as to simplify the algorithms presented by Salowe and Steiger [4]. All algorithms that followed the introduction of the internal buffer by Kronrod in [3] use internal buffers extensively. On... |

16 | Simplified stable merging tasks - Salowe, Steiger - 1987 |

9 |
Stable sorting and merging with optimal space and time bounds
- Pardo
- 1977
(Show Context)
Citation Context .... Horvath [5] managed to derive a stable algorithm with the same asymptotic complexity which, however, had the undesired characteristic of modifying the keys of the elements during the merging. Pardo =-=[6]-=- overcame this obstacle and finally derived an asymptotically optimal algorithm which did not use key modification. Even though asymptotically optimal, because of their complex structure and the large... |

8 |
An optimal ordering algorithm without a field of operation,” Dokl
- Kronrod
- 1969
(Show Context)
Citation Context ...ted sequences A and B of m and n elements, respectively, into a sequence S of N � m n elements requires � O�N time, which is optimal, � but also � uses O�N additional space (see [2], p. 114). Kronrod =-=[3]-=- derived a method of merging two sorted sequences of a total of N elements � in O�N time using only a constant amount of additional space. In doing so, he introduced the important notion of the intern... |

8 | Fast stable merging and sorting in constant extra space
- Huang, Langston
- 1992
(Show Context)
Citation Context ... surprisingly straightforward and practical method for unstable merging that uses (in a more creative way than previously developed algorithms) an ���� internal buffer � of size N �. In a later paper =-=[16]-=-, they managed to make � their algorithm stable. They also used their technique to attack the related problems of duplicate-key extraction [17]. Even though there are algorithms that perform stable me... |

7 |
A simple linear-time algorithm for
- Mannila, Ukkonen
- 1984
(Show Context)
Citation Context ...eral nonoptimal stable algorithms were developed that compromise by using either more time [7–10] or more additional spaces682 A. S YMVONIS [8, 9, 11, 12]. Dvorak and Durian [13], Mannila and Ukkonen =-=[14]-=- and Huang and Langston [15] derived linear time algorithms for unstable in-place merging. The algorithm of Mannila and Ukkonen differs from previously developed algorithms in using an internal buffer... |

5 |
On a Stable Storage Merging Algorithm
- Dudzinski, Dydek
- 1981
(Show Context)
Citation Context ..._EXCHANGE l Y 1 l � 2 is linear in the number of elements participating in the block exchange, reducing their number is something desirable. A more complicated method developed by Dudzinski and Dydek =-=[7]-=- performs the block exchange by using only l � 1 l � 2 gcd�l Y 1 l � 2 assignments, where gcd�l Y 1 l � 2 denotes the greatest common divisor of l1 and l2. We refer the reader to [7] for a description... |

5 |
Stable linear time sublinear space merging
- Dvorak, Durian
- 1987
(Show Context)
Citation Context ...ctical merging algorithms a rich literature has evolved. Several nonoptimal stable algorithms were developed that compromise by using either more time [7–10] or more additional spaces682 A. S YMVONIS =-=[8, 9, 11, 12]-=-. Dvorak and Durian [13], Mannila and Ukkonen [14] and Huang and Langston [15] derived linear time algorithms for unstable in-place merging. The algorithm of Mannila and Ukkonen differs from previousl... |

4 |
Stable Sorting in Asymptotically Optimal Time and Extra Space
- Horvath
- 1978
(Show Context)
Citation Context ...ars.) A description of Kronrod’s algorithm appears in [4] and as the answer to exercise 5.2.4.18 in Knuth’s book ([1], p. 169, 623). Unfortunately, Kronrod’s merging algorithm was not stable. Horvath =-=[5]-=- managed to derive a stable algorithm with the same asymptotic complexity which, however, had the undesired characteristic of modifying the keys of the elements during the merging. Pardo [6] overcame ... |

4 |
Towards an efficient merging
- Dvorak, Durian
- 1986
(Show Context)
Citation Context ...ctical merging algorithms a rich literature has evolved. Several nonoptimal stable algorithms were developed that compromise by using either more time [7–10] or more additional spaces682 A. S YMVONIS =-=[8, 9, 11, 12]-=-. Dvorak and Durian [13], Mannila and Ukkonen [14] and Huang and Langston [15] derived linear time algorithms for unstable in-place merging. The algorithm of Mannila and Ukkonen differs from previousl... |

3 |
SPLITMERGE-A Fast Stable Merging Algorithm
- Carlsson
- 1986
(Show Context)
Citation Context ...ctical merging algorithms a rich literature has evolved. Several nonoptimal stable algorithms were developed that compromise by using either more time [7–10] or more additional spaces682 A. S YMVONIS =-=[8, 9, 11, 12]-=-. Dvorak and Durian [13], Mannila and Ukkonen [14] and Huang and Langston [15] derived linear time algorithms for unstable in-place merging. The algorithm of Mannila and Ukkonen differs from previousl... |

3 |
Stable Duplicate-Key Extraction with Optimal Time and Space Bounds
- Huang, Langston
- 1989
(Show Context)
Citation Context ... an ���� internal buffer � of size N �. In a later paper [16], they managed to make � their algorithm stable. They also used their technique to attack the related problems of duplicate-key extraction =-=[17]-=-. Even though there are algorithms that perform stable merging by using only a constant amount of extra space in linear time, no one succeeds in matching the lower bounds on both the number of compari... |

2 | Some simple in-place merging algorithms - Wong - 1981 |

1 |
Merging by Decomposition Revisited
- Dvorak, Durian
- 1988
(Show Context)
Citation Context |

1 |
Unstable linear O�1� time space merging
- Dvorak, Durian
- 1988
(Show Context)
Citation Context ...iterature has evolved. Several nonoptimal stable algorithms were developed that compromise by using either more time [7–10] or more additional spaces682 A. S YMVONIS [8, 9, 11, 12]. Dvorak and Durian =-=[13]-=-, Mannila and Ukkonen [14] and Huang and Langston [15] derived linear time algorithms for unstable in-place merging. The algorithm of Mannila and Ukkonen differs from previously developed algorithms i... |

1 |
Unstable Linear Time O(1) Space Merging", The Computer Journal 31
- Dvorak, Durian
- 1988
(Show Context)
Citation Context ...Pardo are considered impractical. Several non-optimal stable algorithms that compromise by using either more time [2, 3, 5, 18] or more additional space [1, 3, 5, 4] were developed. Dvorak and Durian =-=[6]-=-, Mannila and Ukkonen [14] and Huang and Langston [8] derived linear time algorithms for unstable in-place merging. The algorithm of Mannila and Ukkonen differs from previously developed algorithms in... |

1 |
Some Simple In-Place Merging Algorithms", Bit 21
- Wong
- 1982
(Show Context)
Citation Context ...ture and the large constant of proportionality, both of the algorithms of Horvath and Pardo are considered impractical. Several non-optimal stable algorithms that compromise by using either more time =-=[2, 3, 5, 18]-=- or more additional space [1, 3, 5, 4] were developed. Dvorak and Durian [6], Mannila and Ukkonen [14] and Huang and Langston [8] derived linear time algorithms for unstable in-place merging. The algo... |

1 |
Towards an E cient Merging
- Dvorak, Durian
- 1986
(Show Context)
Citation Context ...ture and the large constant of proportionality, both of the algorithms of Horvath and Pardo are considered impractical. Several non-optimal stable algorithms that compromise by using either more time =-=[2, 3, 5, 18]-=- or more additional space [1, 3, 5, 4] were developed. Dvorak and Durian [6], Mannila and Ukkonen [14] and Huang and Langston [8] derived linear time algorithms for unstable in-place merging. The algo... |

1 |
Simpli ed Stable Merging Tasks
- Salowe, Steiger
- 1987
(Show Context)
Citation Context ...e locate a block, we swap back the elements to restore it and then to proceed with the merging. Notice that the ordering of the sequence with the \large" elements is not destroyed. Salowe and Steiger =-=[16]-=- used a similar but much more complicated method in their stable in-place linear time merging method. In their paper they also treat the problem that might occur when during the creation of the sequen... |