## Optimal Time-Space Trade-Offs for Sorting (1998)

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Venue: | In Proc. 39th IEEE Sympos. Found. Comput. Sci |

Citations: | 10 - 0 self |

### BibTeX

@INPROCEEDINGS{Pagter98optimaltime-space,

author = {Jakob Pagter and Jakob Pagter and Theis Rauhe and Theis Rauhe},

title = {Optimal Time-Space Trade-Offs for Sorting},

booktitle = {In Proc. 39th IEEE Sympos. Found. Comput. Sci},

year = {1998},

pages = {264--268},

publisher = {IEEE}

}

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### Abstract

We study the fundamental problem of sorting in a sequential model of computation and in particular consider the time-space trade-off (product of time and space) for this problem.

### Citations

259 | Sorting and Searching, volume 3 of The Art of Computer Programming - Knuth - 1973 |

121 |
M.S.Paterson. Selection and sorting with limited storage
- Munro
- 1980
(Show Context)
Citation Context ...ct to trade-offs, these algorithms have the weakness that time cannot be traded for space or vice versa; i.e., the time-space product only holds for "fixed" functions T and S of n. Munro and=-= Paterson [14]-=- gave the first time-space focused algorithm, realising T \Delta S = O(n 2 log n), but still the time-space product is only realisable 2 for S = \Theta(log n). The first fully scalable, and till now t... |

82 |
The Complexity of Computing
- Savage
- 1976
(Show Context)
Citation Context ...r opinion that it is of practical as well as theoretical relevance. Related work. A general survey of time-space trade-offs is given by Borodin in [12]. An introduction to the area is given by Savage =-=[13]-=-. Upper bounds. Classical sorting algorithms like QuickSort and MergeSort, have T \Delta S = O(n 2 log 2 n). This stems from the fact that space is measured in bits, and these algorithm use O(n) log-s... |

54 | A time-space tradeoff for sorting on a general sequential model of computation
- BORODIN, COOK
- 1980
(Show Context)
Citation Context ...vestigation of the trade-off between the two most fundamental complexity measures; time and space --- pioneered by Cobham [3]. Accordingly, time-space trade-offs for sorting is a much studied problem =-=[4, 5, 6, 7, 8, 9]-=-. Despite the successes of this work, a discrepancy of at least a logarithmic factor (referred to in [4, 6, 7, 10, 11]) between the best known upper bound --- O(n 2 log n) [5], and the best known lowe... |

41 |
The Recognition Problem for the Set of Perfect Squares
- COBHAM
- 1966
(Show Context)
Citation Context ...s more recent work in the area). One fruitful line of research has been the investigation of the trade-off between the two most fundamental complexity measures; time and space --- pioneered by Cobham =-=[3]-=-. Accordingly, time-space trade-offs for sorting is a much studied problem [4, 5, 6, 7, 8, 9]. Despite the successes of this work, a discrepancy of at least a logarithmic factor (referred to in [4, 6,... |

27 | A general sequential time-space tradeoff for finding unique elements
- Beame
- 1991
(Show Context)
Citation Context ...vestigation of the trade-off between the two most fundamental complexity measures; time and space --- pioneered by Cobham [3]. Accordingly, time-space trade-offs for sorting is a much studied problem =-=[4, 5, 6, 7, 8, 9]-=-. Despite the successes of this work, a discrepancy of at least a logarithmic factor (referred to in [4, 6, 7, 10, 11]) between the best known upper bound --- O(n 2 log n) [5], and the best known lowe... |

25 |
Near-optimal time-space tradeoff for element distinctness
- Yao
- 1988
(Show Context)
Citation Context ...am [3]. Accordingly, time-space trade-offs for sorting is a much studied problem [4, 5, 6, 7, 8, 9]. Despite the successes of this work, a discrepancy of at least a logarithmic factor (referred to in =-=[4, 6, 7, 10, 11]-=-) between the best known upper bound --- O(n 2 log n) [5], and the best known lower bound --- \Omega\Gamma n 2 ) [4] --- remained. The main contribution of this paper is an algorithm which closes this... |

24 | A time-space tradeoff for sorting on nonoblivious machines
- Borodin, Fischer, et al.
- 1981
(Show Context)
Citation Context ...vestigation of the trade-off between the two most fundamental complexity measures; time and space --- pioneered by Cobham [3]. Accordingly, time-space trade-offs for sorting is a much studied problem =-=[4, 5, 6, 7, 8, 9]-=-. Despite the successes of this work, a discrepancy of at least a logarithmic factor (referred to in [4, 6, 7, 10, 11]) between the best known upper bound --- O(n 2 log n) [5], and the best known lowe... |

22 |
Sorting and Searching, vol. 3 of The Art of Computer Programming (2nd edition
- Knuth
- 1998
(Show Context)
Citation Context ...oundation. 1 1 Introduction Motivation and results. The complexity of sorting is a classical problem in computer science which has provided a wide scope of both algorithms and lower bounds (see Knuth =-=[1]-=- and Andersson [2] for an overview of classical as well as more recent work in the area). One fruitful line of research has been the investigation of the trade-off between the two most fundamental com... |

16 | A time-space tradeoff for element distinctness
- Borodin, Fich, et al.
- 1987
(Show Context)
Citation Context ...am [3]. Accordingly, time-space trade-offs for sorting is a much studied problem [4, 5, 6, 7, 8, 9]. Despite the successes of this work, a discrepancy of at least a logarithmic factor (referred to in =-=[4, 6, 7, 10, 11]-=-) between the best known upper bound --- O(n 2 log n) [5], and the best known lower bound --- \Omega\Gamma n 2 ) [4] --- remained. The main contribution of this paper is an algorithm which closes this... |

15 |
Time Space Tradeoffs (Getting Closer to the Barrier
- BORODIN
- 1993
(Show Context)
Citation Context ...le, and involves only small constants, hence it is our opinion that it is of practical as well as theoretical relevance. Related work. A general survey of time-space trade-offs is given by Borodin in =-=[12]-=-. An introduction to the area is given by Savage [13]. Upper bounds. Classical sorting algorithms like QuickSort and MergeSort, have T \Delta S = O(n 2 log 2 n). This stems from the fact that space is... |

15 |
Selection and Sorting with
- Munro, Paterson
- 1980
(Show Context)
Citation Context ...ct to trade-offs, these algorithms have the weakness that time cannot be traded for space or vice versa; i.e., the time-space product only holds for “fixed” functions T and S of n. Munro and Paterson =-=[14]-=- gave the first time-space focused algorithm, realising T ·S =O(n2log n), but still the time-space product is only realisable 2sfor S =Θ(logn). The first fully scalable, and till now the best upper bo... |

12 |
Two time-space tradeoffs for element distinctness
- Karchmer
- 1986
(Show Context)
Citation Context ...rs in the algorithms workspace times the word size. Branching programs. Most time-space trade-offs lower bounds for sorting and similar problems are proved for the non-uniform branching program model =-=[4, 6, 7, 8, 9, 10, 11, 15, 16]-=-. Branching programs are mainly used in two variants: 1. Comparison based branching programs (also known as decision branching programs); this is a comparison based model strong enough to real-time 4 ... |

8 | Sorting and searching revisited - Andersson - 1996 |

7 |
Upper Bounds for Time-Space Trade-Offs in Sorting and Selection
- FREDERICKSON
- 1980
(Show Context)
Citation Context ...log 2 n, for appropriate positive constants c 1 and c 2 . The range in which we can realise this trade-off is not maximal --- a factor log n is missing. Combining our ideas with those of Frederickson =-=[5]-=- we can remove this logarithmic factor, and obtain the trade-off in the maximal range: Theorem 1 There exists positive constants c 1 and c 2 such that for any S in the interval c 1 log nsSsc 2 n= log ... |

5 |
SCHNITGER: Three applications of Kolmogorov-complexity
- REISCH, G
- 1982
(Show Context)
Citation Context |

5 |
On the Time-Space Tradeoff for Sorting with Linear Queries
- YAO
(Show Context)
Citation Context |

2 |
Time-Space Tradeoffs for Set Operations
- Patt-Shamir, Peleg
- 1993
(Show Context)
Citation Context ...ny comparison based branching program solving the element distinctness problem on n keys, must have T \Delta S = \Omega\Gamma n 2\Gammaffl(n) ), where ffl(n) is decreasing in n. Patt-Shamir and Peleg =-=[15]-=- studies a number of other set problems, including: set complementation (given a set X from some finite subset of an ordered universe U , output X C ), set subtraction (given X and Y , output X n Y ),... |

2 |
Sorting and Searching Revisited,” in Algorithm Theory
- Andersson
- 1996
(Show Context)
Citation Context ...roduction Motivation and results. The complexity of sorting is a classical problem in computer science which has provided a wide scope of both algorithms and lower bounds (see Knuth [1] and Andersson =-=[2]-=- for an overview of classical as well as more recent work in the area). One fruitful line of research has been the investigation of the trade-off between the two most fundamental complexity measures; ... |

1 |
Sorting and Searching Revisited," in Algorithm Theory
- Andersson
- 1996
(Show Context)
Citation Context ...roduction Motivation and results. The complexity of sorting is a classical problem in computer science which has provided a wide scope of both algorithms and lower bounds (see Knuth [1] and Andersson =-=[2]-=- for an overview of classical as well as more recent work in the area). One fruitful line of research has been the investigation of the trade-off between the two most fundamental complexity measures; ... |