Advertisement

Algorithmica

, Volume 25, Issue 4, pp 438–458 | Cite as

Optimal Deterministic Sorting and Routing on Grids and Tori with Diagonals

  • M. Kunde
  • R. Niedermeier
  • K. Reinhardt
  • P. Rossmanith

Abstract.

We present deterministic sorting and routing algorithms for grids and tori with additional diagonal connections. For large loads ( \(h\geq 12\) ), 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 \(h\geq 1\) . 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.

Key words. Parallel architectures, Mesh-connected processor arrays, Diagonal connections, Parallel algorithms, Sorting, Routing. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York Inc. 1999

Authors and Affiliations

  • M. Kunde
    • 1
  • R. Niedermeier
    • 2
  • K. Reinhardt
    • 2
  • P. Rossmanith
    • 3
  1. 1.Fakultät für Informatik und Automatisierung, Technische Universität Ilmenau, Postfach 0565, D-98684 Ilmenau, Germany. Manfred.Kunde@theoinf.tu-ilmenau.de.DE
  2. 2.Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Germany. niedermr@informatik.uni-tuebingen.de, reinhard@informatik.uni-tuebingen.de.DE
  3. 3.Fakultät für Informatik, Technische Universität München, Arcisstrasse 21, D-80290 München, Germany. rossmani@informatik.tu-muenchen.de.DE

Personalised recommendations