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On Sorting Strings in External Memory
, 1997
"... ) Lars Arge Paolo Ferragina y Roberto Grossi z Jeffrey Scott Vitter x Abstract. In this paper we address for the first time the I/O complexity of the problem of sorting strings in external memory, which is a fundamental component of many largescale text applications. In the standard unitcost RAM c ..."
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Cited by 27 (12 self)
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) Lars Arge Paolo Ferragina y Roberto Grossi z Jeffrey Scott Vitter x Abstract. In this paper we address for the first time the I/O complexity of the problem of sorting strings in external memory, which is a fundamental component of many largescale text applications. In the standard unitcost RAM comparison model, the complexity of sorting K strings of total length N is \Theta(K log 2 K+N). By analogy, in the external memory (or I/O) model, where the internal memory has size M and the block transfer size is B, it would be natural to guess that the I/O complexity of sorting strings is \Theta( K B log M=B K B + N B ), but the known algorithms do not come even close to achieving this bound. Our results show, somewhat counterintuitively, that the I/O complexity of string sorting depends upon the length of the strings relative to the block size. We first consider a simple comparison I/O model, where one is not allowed to break the strings into their characters, and we sho...
On sorting strings in external memory (extended abstract
 In STOC ’97: Proceedings of the twentyninth annual ACM symposium on Theory of computing
, 1997
"... Abstract. In this paper we address for the first time the I/O complexity of the problem of sorting strings in external memory, which is a fundamental component of many largescale text applications. In the standard unitcost RAM comparison model, the complexity of sorting K strings of total length N ..."
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Cited by 3 (0 self)
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Abstract. In this paper we address for the first time the I/O complexity of the problem of sorting strings in external memory, which is a fundamental component of many largescale text applications. In the standard unitcost RAM comparison model, the complexity of sorting K strings of total length N is (K log2 K +N). By analogy, in the external memory (or I/O) model, where the internal memory has size M and the block transfer size is B, it would be natural to guess that the I/O complexity of sorting strings is ( K B logM=B K N
unknown title
"... Abstract We show that a unitcost RAM with a word length of w bitscan sort n integers in the range 0: : 2w \Gamma 1 in O(n log log n)time, for arbitrary w * log n, a significant improvementover the bound of O(nplog n) achieved by the fusion treesof Fredman and Willard. Provided that w * (log n)2+ffl ..."
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Abstract We show that a unitcost RAM with a word length of w bitscan sort n integers in the range 0: : 2w \Gamma 1 in O(n log log n)time, for arbitrary w * log n, a significant improvementover the bound of O(nplog n) achieved by the fusion treesof Fredman and Willard. Provided that w * (log n)2+ffl, forsome fixed ffl? 0, the sorting can even be accomplished inlinear expected time with a randomized algorithm. Both of our algorithms parallelize without loss on a unitcost PRAM with a word length of w bits. The first one yieldsan algorithm that uses O(log n) time and O(n log log n) operations on a deterministic CRCW PRAM. The second one yields an algorithm that uses O(log n) expected time and O(n) expected operations on a randomized EREW PRAM,provided that w * (log n)2+ffl for some fixed ffl? 0.Our deterministic and randomized sequential and parallel algorithms generalize to the lexicographic sorting problemof sorting multipleprecision integers represented in several words. 1 Introduction Sorting is one of the most fundamental computational problems, and n keys can be sorted in O(n log n) time by anyof a number of wellknown sorting algorithms. These algorithms operate in the comparisonbased setting, i.e., they obtain information about the relative order of keys exclusively through pairwise comparisons. It is easy to show that a running time of
Arne Andersson
"... We show that a unitcost RAM with a word length of w bits can sort n integers in the range 0 : : 2 w \Gamma 1 in O(n log log n) time, for arbitrary w log n, a significant improvement over the bound of O(n p log n) achieved by the fusion trees of Fredman and Willard. Provided that w (log n) 2+ ..."
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We show that a unitcost RAM with a word length of w bits can sort n integers in the range 0 : : 2 w \Gamma 1 in O(n log log n) time, for arbitrary w log n, a significant improvement over the bound of O(n p log n) achieved by the fusion trees of Fredman and Willard. Provided that w (log n) 2+ffl for some fixed ffl ? 0, the sorting can even be accomplished in linear expected time with a randomized algorithm. Both of our algorithms parallelize without loss on a unitcost PRAM with a word length of w bits. The first one yields an algorithm that uses O(log n) time and O(n log log n) operations on a deterministic CRCW PRAM. The second one yields an algorithm that uses O(log n) expected time and O(n) expected operations on a randomized EREW PRAM, provided that w (log n) 2+ffl for some fixed ffl ? 0. Our deterministic and randomized sequential and parallel algorithms generalize to the lexicographic sorting problem of sorting multipleprecision integers represented in several words...