Computer Science in Perspective pp 115-127 | Cite as

# Fast Merging and Sorting on a Partitioned Optical Passive Stars Network

- 3 Citations
- 440 Downloads

## Abstract

We present fast algorithms for merging and sorting of data on a multiprocessor system connected through a *Partitioned Optical Passive Stars (POPS)* network. In a *POPS(d, g)* network there are *n* = *dg* processors and they are divided into g groups of d processors each. There is an optical passive star (OPS) coupler between every pair of groups. Each OPS coupler can receive an optical signal from any one of its source nodes and broadcast the signal to all the destination nodes. The time needed to perform this receive and broadcast is referred to as a *slot* and the complexity of an algorithm using the POPS network is measured in terms of number of slots it uses. Our sorting algorithm is more efficient compared to a simulated hypercube sorting algorithm on the POPS.

## Keywords

Source Node Destination Node Binary Search Sorting Algorithm Large Group Size## Preview

Unable to display preview. Download preview PDF.

## References

- 1.P. Berthomé and A. Ferreira, “Improved embeddings in POPS networks through stack-graph models”,
*Proc. Third International Workshop on Massively Parallel Processing Using Optical Interconnections*, pp. 130–135, 1996.Google Scholar - 2.P. Berthomé, J. Cohen and A. Ferreira, “Embedding tori in partitioned optical passive stars networks”,
*Proc. Fourth International Colloquium on Structural Information and Communication Complexity (Sirocco’ 97)*, pp. 40–52, 1997.Google Scholar - 3.D. Chiarulli, S. Levitan, R. Melhem, J. Teza and G. Gravenstreter, “ePartitioned optical passive star (POPS) multiprocessor interconnection networks with distributed control”,
*Journal of Lightwave Technology*,**14**(7), pp. 1901–1612, 1996.CrossRefGoogle Scholar - 4.R. Cypher and G. Plaxton, “Deterministic sorting in nearly logarithmic time on the hypercube and related computers”,
*Proc. 22nd Annual ACM Symposium on Theory of Computing*, pp. 193–203, 1990.Google Scholar - 5.A. Datta and S. Soundaralakshmi, “Basic operations on a partitioned optical passive stars net-work with large group size”,
*Proc. 2002 International Conference on Computational Science*, Amsterdam, Lecture Notes in Computer Science, Springer-Verlag, Vol. 2329, pp. 306–315, 2002.Google Scholar - 6.A. Datta and S. Soundaralakshmi, “Summation and routing on a partitioned optical passive stars network with large group size”, Manuscript, 2002.Google Scholar
- 7.G. Gravenstreter and R. Melhem, “Realizing common communication patterns in partitioned optical passive stars (POPS) networks”,
*IEEE Trans. Computers*,**47**(9), pp. 998–1013, 1998.Google Scholar - 8.G. Gravenstreter, R. Melhem, D. Chiarulli, S. Levitan and J. Teza, “The partitioned optical passive stars (POPS) topology”,
*Proc. Ninth International Parallel Processing Symposium*, IEEE Computer Society, pp. 4–10, 1995.Google Scholar - 9.F. T. Leighton,
*Introduction to Parallel Algorithms and Architectures: Arrays-Trees-Hypercubes*, Morgan-Kaufman, San Mateo, 1992.zbMATHGoogle Scholar - 10.R. Melhem, G. Gravenstreter, D. Chiarulli and S. Levitan, “The communication capabilities of partitioned optical passive star networks”,
*Parallel Computing Using Optical Interconnections*, K. Li, Y. Pan and S. Zheng (Eds), Kluwer Academic Publishers, pp. 77–98, 1998.Google Scholar - 11.A. Mei and R. Rizzi, “Routing permutations in partitioned optical passive stars networks”,
*Proc. 16th International Parallel and Distributed Processing Symposium*, Fort Lauderdale, Florida, IEEE Computer Society, April 2002.Google Scholar - 12.S. Ranka and S. Sahni,
*Hypercube Algorithms with Applications to Image Processing and Pattern Recognition*, Springer-Verlag, New York, 1990.zbMATHGoogle Scholar - 13.S. Sahni, “The partitioned optical passive stars network: Simulations and fundamental operations”,
*IEEE Trans. Parallel and Distributed Systems*,**11**(7), pp. 739–748, 2000.MathSciNetCrossRefGoogle Scholar - 14.S. Sahni, “Matrix multiplication and data routing using a partitioned optical passive stars network”,
*IEEE Trans. Parallel and Distributed Systems*,**11**(7), pp. 720–728, 2000.MathSciNetCrossRefGoogle Scholar - 15.S. Sahni, “Models and algorithms for optical and optoelectronic parallel computers”,
*Inter-national Journal of Foundations of Computer Science*,**12**(3), pp. 249–264, 2001.CrossRefGoogle Scholar - 16.F. T. Leighton,
*Introduction to Parallel Algorithms and Architectures: Arrays-Trees-Hypercubes*, Morgan-Kaufman, San Mateo, 1992.zbMATHGoogle Scholar