Abstract
Sorting on interconnection networks has been solved ‘optimally’. However, the ‘lower-order’ terms are so large that they dominate the overall time-consumption for many practical problem sizes. Particularly for deterministic algorithms, this is a serious problem. In this paper a refined deterministic sampling strategy is presented, by which the additional term of the presented deterministic sorting algorithm is hardly larger than the one of the best randomized algorithm.
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References
Blelloch, G. E., C. E. Leiserson, B. M. Maggs, C. G. Plaxton, S. J. Smith, M. Zagha, ‘A Comparison of Sorting Algorithms for the Connection Machine CM-2,’ Proc. 3rd SPAA, pp. 3–16. ACM, 1991.
Berthomé, P., A. Ferreira, B.M. Maggs, S. Perennes, C.G. Plaxton, 'sorting-Based Selection Algorithms for Hypercubic Networks,’ Proc. 7th IPPS, pp. 89–95, IEEE, 1993.
Chaudhuri, S., T Hagerup, R. Raman, ‘Approximate and Exact Deterministic Parallel Selection,’ Proc. 18th MFCS, LNCS 711, pp. 352–361, Springer-Verlag, 1993.
Cole, C., C.K. Yap, ‘A Parallel Median Algorithm,’ IPL, 20, pp. 137–139,1985.
Diekmann, R., J. Gehring, R. Lüling, B. Monien M. Nübel, R. Wanka, 'sorting Large Data Sets on a Massively Parallel System,’ Proc. 6th SPDP, pp. 2–9, IEEE, 1994.
Hagerup, T., C. Rob, ‘A Guided Tour of Chemoff Bounds,’ Inf. Proc. Lett. 33, 305–308, 1990.
Hightower, W.L., J.F. Prins, J.H. Reif, ‘Implementations of Randomized Sorting on Large Parallel Machines,’ Proc. 4th Symp. on Parallel Algorithms and Architectures, pp. 158–167, ACM, 1992.
Kaklamanis, C., D. Krizanc, L. Narayanan, Th. Tsantilas, ‘Randomized Sorting and Selection on Mesh Connected Processor Arrays,’ Proc. 3rd SPAA, pp. 17–28, ACM, 1991.
Kaufmann, M., S. Rajasekaran, J.F. Sibeyn, ‘Matching the Bisection Bound for Routing and Sorting on the Mesh,’ Proc. 4th Symp. on Parallel Algorithms and Architectures, pp. 31–40, ACM, 1992.
Kaufmann, M., J.F. Sibeyn, ‘Randomized Multipacket Routing and Sorting on Meshes,’ Algorithinica, 17, pp. 224–244, 1997.
Kaufmann, M., J.F. Sibeyn, T Suel, ‘Derandomizing Algorithms for Routing and Sorting on Meshes,’ Proc. 5th Symp. on Discrete Algorithms, pp. 669–679 ACM-SIAM, 1994.
Kunde, M., ‘Block Gossiping on Grids and Tori: Deterministic Sorting and Routing Match the Bisection Bound,’ Proc. 1st ESA, LNCS 726, pp. 272–283, Springer-Verlag, 1993.
Leighton, FT, ‘Tight Bounds on the Complexity of Parallel Sorting,’ IEEE Transactions on Computers, C-34(4), pp. 344–354,1985.
Leighton, T., ‘Average Case Analysis of Greedy Routing Algorithms on Arrays,’ Proc. 2nd Syrnp. on Parallel Algorithms and Architectures, pp. 2–10, ACM, 1990.
Leighton, FT, Introduction to Parallel Algorithms andArchitectures: Arrays, Trees and Hypercubes, Morgan Kaufmann,1991.
Reif, J.H., L.G. Valiant, ‘A logarithmic time sort for linear size networks,’ Journal of the ACM, 34(1), pp. 68–76, 1987.
Reischuk, R., ‘Probabilistic Parallel Algorithms for Sorting and Selection,’ SIAM Journal of Compttting, 14, pp. 396–411, 1985.
Schnorr, C.P., A. Shamir, 'sAn Optimal Sorting Algorithm for Mesh Connected Computers', Proc. 18th Symp. on Theory of Computing, pp. 255–263, ACM, 1986.
Sibeyn, J.F, ‘Desnakification of Mesh Sorting Algorithms,’ accepted 9-1996 for SIAM Journal on Computing. Preliminary version in Proc. 2nd European Symp. on Algorithms, LNCS 855, pp. 377-390, Springer-Verlag, 1994. Full version in Techn. Rep. MPI-1-94-102, Max-Planck-Institut für Informatik, Saarbrücken,Germany, 1994.
Sibeyn, J.F, 'sample Sort on Meshes,’ Techn. Rep. MPI-1-95-1012, Max-Planck Institut für Informatik, Saarbrücken, Germany, 1995.
Valiant, L. G.. ‘A Scheme for Fast Parallel Communication,’ SIAM Journal on Computing, 11, pp. 350–361,1982. *** DIRECT SUPPORT *** A0008C42 00014
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Sibeyn, J.F. (1997). Sample sort on meshes. In: Lengauer, C., Griebl, M., Gorlatch, S. (eds) Euro-Par'97 Parallel Processing. Euro-Par 1997. Lecture Notes in Computer Science, vol 1300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0002762
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DOI: https://doi.org/10.1007/BFb0002762
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