Sorting in linear time?

Andersson, Arne; Hagerup, Torben; Nilsson, S.; Raman, Rajeev

doi:10.1145/225058.225173

Cited by 94 publications

(78 citation statements)

References 13 publications

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“…Thus, we propose that we use an array of size 2 inst･ead of the Q-heap since the size ICIogn)i/'41 s{ Lbi!41 E{ 2 where b denotes the Xie liave some small probiems to imp],ementi the construction of 7". First, in the aonstruct/ion of 7', Thorup used a puacked TneTying sort pi'oposed in[2] and[1]. It is too complicated tc) implement, but in this problem it is used only for n < b and for other n the bucket sort, is used, Therefore, we assume…”

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confidence: 99%

Practical Efficiency of the Linear-Time Algorithm for the Single Source Shortest Path Problem

Asano

Imai

2000

JORSJ

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Abstrrzct Thorup's linear-tirne algorithm for the single source shoTtest path problem consists of two phases[ u consLruction phase of constructing a data structure suitable for a shorte$t/ path search from a given query source s; and a search phase of finding shertest･ paths from the query source s to al1 vertices using the data structure constructed in construction phase, Since once the data structure is eonstrllcted, it can be repeaLedly used tbr shortest path searches from given query sources, [I]horup]s algorithm has a nice feature not only on its linear time cornplexity but aiso on its dat,a structure suitable for a repetitive mode of queries (not single gtie'cy). In this paper, we evaluate the practicaE eMciellcy of the Thorup's ]inear-time algorithm through comptit/ationai experirnents c:omparing wit,h some o'f well kllown preyiou$ algorithms. In particular, we eva]llate Thorup's algorithm makily rrom t,he yiewpoiiit of repetitive rnode of queries.

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confidence: 99%

Practical Efficiency of the Linear-Time Algorithm for the Single Source Shortest Path Problem

Asano

Imai

2000

JORSJ

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“…One can remark that the probability of using a single excitation to go from one determinant to the next one in the list is very high. The sort is performed in a linear time with respect to

N_{det}^{↑}

and

N_{det}^{↓}

thanks to the radix sort algorithm . Then, duplicate determinants are filtered out by searching for duplicates among determinants giving the same key ω .…”

Section: Algorithm and Implementationmentioning

confidence: 99%

“…The sort is performed in a linear time with respect to N " det and N # det thanks to the radix sort algorithm. [12] Then, duplicate determinants are filtered out by searching for duplicates among determinants giving the same key x. At this point, we have two spin-specific lists of sorted determinants containing, respectively, N " det and N # det unique determinants.…”

Section: Algorithm and Implementationmentioning

confidence: 99%

Quantum Monte Carlo with very large multideterminant wavefunctions

et al. 2016

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An algorithm to compute efficiently the first two derivatives of (very) large multideterminant wavefunctions for quantum Monte Carlo calculations is presented. The calculation of determinants and their derivatives is performed using the Sherman-Morrison formula for updating the inverse Slater matrix. An improved implementation based on the reduction of the number of column substitutions and on a very efficient implementation of the calculation of the scalar products involved is presented. It is emphasized that multideterminant expansions contain in general a large number of identical spin-specific determinants: for typical configuration interaction-type wavefunctions the number of unique spin-specific determinants Ndetσ ( σ=↑,↓) with a non-negligible weight in the expansion is of order O(Ndet). We show that a careful implementation of the calculation of the Ndet -dependent contributions can make this step negligible enough so that in practice the algorithm scales as the total number of unique spin-specific determinants,  Ndet↑+Ndet↓, over a wide range of total number of determinants (here, Ndet up to about one million), thus greatly reducing the total computational cost. Finally, a new truncation scheme for the multideterminant expansion is proposed so that larger expansions can be considered without increasing the computational time. The algorithm is illustrated with all-electron fixed-node diffusion Monte Carlo calculations of the total energy of the chlorine atom. Calculations using a trial wavefunction including about 750,000 determinants with a computational increase of ∼400 compared to a single-determinant calculation are shown to be feasible. © 2016 Wiley Periodicals, Inc.

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“…From assumption 4 it follows that any sorting method must use at least ~2(n log 2 n) time (see, e.g., [11,Section 5.3]). However, without this assumption n integers can be sorted in O(n log 2 log 2 n) time [1], or even in O(n) time if integers are small (see, e.g., [11, pp. 99-102]).…”

Section: Introductionmentioning

confidence: 99%

A meticulous analysis of mergesort programs

Katajainen

Träff

1997

Lecture Notes in Computer Science

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The efficiency of mergesort programs is analysed under a simple unit-cost model. In our analysis the time performance of the sorting programs includes the costs of key comparisons, element moves and address calculations. The goal is to establish the best possible time-bound relative to the model when sorting n integers. By the well-known information-theoretic argument n log 2 n-O(n) is a lower bound for the integer-sorting problem in our framework. New implementations for two-way and four-way bottom-up mergesort are given, the worst-case complexities of which are shown to be bounded by 5.5nlog 2 n + O(n) and 3.25nlog 2 n + O(n), respectively. The theoretical findings are backed up with a series of experiments which show the practical relevance of our analysis when implementing library routines for internal-memory computations.

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Sorting in linear time?

Cited by 94 publications

References 13 publications

Practical Efficiency of the Linear-Time Algorithm for the Single Source Shortest Path Problem

Practical Efficiency of the Linear-Time Algorithm for the Single Source Shortest Path Problem

Quantum Monte Carlo with very large multideterminant wavefunctions

A meticulous analysis of mergesort programs

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