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On Sorting Strings in External Memory (Extended 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 strings of total ¥ length ¦¨§©¤��� ..."
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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 strings of total ¥ length ¦¨§©¤���������¤��¨¥� � is. By analogy, in the external memory (or I/O) model, where the internal memory has � size and the block transfer size � is, it would be natural to guess that the I/O complexity of sorting strings ¦¨§������������ � � �������� � is, 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
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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 ..."
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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
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"... Widespread availability of location aware devices (such as GPS receivers) promotes capture of detailed movement trajectories of people, animals, vehicles and other moving objects, opening new options for a better understanding of the processes involved. In this paper we investigate spatiotemporal mo ..."
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Widespread availability of location aware devices (such as GPS receivers) promotes capture of detailed movement trajectories of people, animals, vehicles and other moving objects, opening new options for a better understanding of the processes involved. In this paper we investigate spatiotemporal movement patterns in large tracking data sets. We present a natural definition of the pattern ‘one object is leading others’, and discuss how such leadership patterns can be computed from a group of moving entities. The proposed definition is based on behavioural patterns discussed in the behavioural ecology literature. We also present several algorithms for computing the pattern, and they are analysed both theoretically and experimentally.