Optimal average case sorting on arrays

Kunde, Manfred; Niedermeier, Rolf; Reinhardt, Klaus; Rossmanith, Peter

doi:10.1007/3-540-59042-0_100

Cited by 6 publications

(9 citation statements)

References 9 publications

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“…We improved this to optimal hn/6 + o(n) steps using completely new techniques. For deterministic average case sorting for grids and tori with and without diagonals, one can obtain results that, in general, are twice as fast as in the worst case [12].…”

Section: Results For Small Loads Using Concentration Techniquesmentioning

confidence: 97%

“…By using a different sorting scheme with only one all-to-all mapping, it is possible to halve the running times of many of our algorithms in the average case [12]. Particularly, one can obtain, in the average, optimal h-h sorting and routing algorithms for tori and grids with diagonals for all h (see [12]).…”

Section: Discussionmentioning

confidence: 99%

“…Particularly, one can obtain, in the average, optimal h-h sorting and routing algorithms for tori and grids with diagonals for all h (see [12]). …”

Section: Discussionmentioning

confidence: 99%

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Optimal Deterministic Sorting and Routing on Grids and Tori with Diagonals

et al. 1999

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We present deterministic sorting and routing algorithms for grids and tori with additional diagonal connections. For large loads (h ≥ 12), where each processor has at most h data packets in the beginning and in the end, the sorting problem can be solved in optimal hn/6 + o(n) and hn/12 + o(n) steps for grids and tori with diagonals, respectively. For smaller loads, we present a new concentration technique that yields very fast algorithms for h < 12. For a load of 1, the previously most studied case, sorting only takes 1.2n + o(n) steps and routing only 1.1n + o(n) steps. For tori, we can present optimal algorithms for all loads h ≥ 1. The above algorithms all use a constant-size memory for all processors and never copy or split packets, a property that the corresponding lower bounds make use of.If packets may be copied, 1-1 sorting can be done in only 2n/3 + o(n) on a torus with diagonals.Generally gaining a speedup of 3 by only doubling the number of communication links compared with a grid without diagonals, our work suggests building grids and tori with diagonals.

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Section: Results For Small Loads Using Concentration Techniquesmentioning

confidence: 97%

Section: Discussionmentioning

confidence: 99%

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Optimal Deterministic Sorting and Routing on Grids and Tori with Diagonals

et al. 1999

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“…It is not hard to perform k k routing twice as fast for average case inputs; just omit the randomization phase. An analysis is given in [161]. In [145], several ideas are combined to obtain an algorithm with routing time close to knÂ4 for average case inputs while never exceeding knÂ2.…”

Section: On-line Routingmentioning

confidence: 99%

Packet Routing in Fixed-Connection Networks: A Survey

Grammatikakis

Hsu

Kraetzl

et al. 1998

Journal of Parallel and Distributed Computing

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“…For all 0 i n 4 3 , j 7 ! i + j div n 2 3 mod n 2 3 n 2 3 + i div n 2 3 + j mod n 2 3 mod n 2 3 is a permutation of the set n 4 3 .…”

Section: Proof(sketch)mentioning

confidence: 99%

Sorting on the OTIS-mesh

Osterloh

Proceedings 14th International Parallel and Distributed Processing Symposium. IPDPS 2000

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In this paper we present sorting algorithms on the re-a network with diameter 4 p N , 3 consisting of N connected meshes of size p N p N. We show that k-k sorting can be done in 8 p N + ON 1 3 steps for k = 1; 2; 3; 4 and in 2k p N + OkN 1 3 steps for k 4 with constant buffersize for all k. We show how our algorithms can be modified to achieve 4 p N+ON 1 3 steps for k = 1 ; 2; 3; 4 and k p N+OkN 1 3 steps for k 4 in the average case. Finally we show a lower bound of maxf4 p N ; 1 p 2 k p Ng steps for k-k sorting.

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Optimal average case sorting on arrays

Cited by 6 publications

References 9 publications

Optimal Deterministic Sorting and Routing on Grids and Tori with Diagonals

Optimal Deterministic Sorting and Routing on Grids and Tori with Diagonals

Packet Routing in Fixed-Connection Networks: A Survey

Sorting on the OTIS-mesh

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