Randomized Multipacket Routing and Sorting on Meshes

Algorithmica (New York)

Volumn 17, Issue 3, 1997, Pages 224-244

  Kaufmann, M ^a   Sibeyn, J F ^b  

^a UNIVERSITY OF TÜBINGEN   (Germany)

^b MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

Author keywords

Packet routing; Parallel algorithms; Randomization; Sorting

Indexed keywords

EID: 0000733243     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02523190     Document Type: Article

References (32)

1. Chernoff, H., A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the Sum of Observations, Annals of Mathematical Statistics, 23, 1952, 493-507.
2. Chlebus, B, S., M. Kaufmann, J. F. Sibeyn, Deterministic Permutation Routing on Meshes, Proc. 5th Symposium on Parallel and Distributed Processing, pp. 814-821, IEEE, 1993.
3. Felperin, S., P. Raghavan, E. Upfal, A Theory of Wormhole Routing in Parallel Computers, Proc. 33rd Symposium on Foundations of Computer Science, pp. 563-572, IEEE, 1992.
4. Hagerup, T., C. Rüb, A Guided Tour of Chernoff Bounds, Information Processing Letters, 33, 1990, 305-308.
5. JáJá, J., An Introduction to Parallel Algorithms, Addison-Wesley, Reading, MA, 1992.
6. Kaklamanis, C., D. Krizanc, Optimal Sorting on Mesh-Connected Processor Arrays, Proc. 4th Symposium on Parallel Algorithms and Architectures, pp. 50-59, ACM, 1992.
7. Kaklamanis, C., D. Krizanc, L. Narayanan, Th. Tsantilas, Randomized Sorting and Selection on Mesh Connected Processor Arrays, Proc. 3rd Symposium on Parallel Algorithms and Architectures, pp. 17-28, ACM, 1991.
8. Kaufmann, M., S. Rajasekaran, J. F. Sibeyn, Matching the Bisection Bound for Routing and Sorting on the Mesh, Proc. 4th Symposium on Parallel Algorithms and Architectures, pp. 31-40, ACM, 1992.
9. Kaufmann, M., J. F. Sibeyn, Optimal Multi-Packet Routing on the Torus, Proc. 3rd Scandinavian Workshop on Algorithm Theory. LNCS 621, pp. 118-129, Springer-Verlag, Berlin, 1992.
10. Kaufmann, M., J. F. Sibeyn, Deterministic Routing on Circular Arrays. Proc. 4th Symposium on Parallel and Distributed Processing, pp. 376-383, IEEE, 1992.
11. Kumar, M., D. Hirschberg, An Efficient Implementation of Batcher's Odd-Even Merge Algorithm and its Application to Parallel Sorting Schemes, IEEE Transactions on Computers, 32, 1983, 141-150.
12. Kunde, M., Routing and Sorting on Mesh Connected Processor Arrays, Proc. VLSI Algorithms and Architectures, LNCS 319, pp. 423-433, Springer-Verlag, Berlin, 1988.
13. Kunde, M., Concentrated Regular Data Streams on Grids: Sorting and Routing Near to the Bisection Bound, Proc. 31st Symposium on Foundations of Computer Science, pp. 141-150, IEEE, 1991.
14. Kunde, M. Balanced Routing: Towards the Distance Bound on Grids, Proc. 3rd Symposium onfaralki. Algorithms and Architectures, pp. 260-271, ACM, 1991.
15. Kunde, M., T. Tensi, Multi-Packet Routing on Mesh Connected Processor Arrays, Proc. Symposium on. Parallel Algorithms and Architectures, pp. 336-343, ACM. 1989.
16. Leighton, T., Average Case Analysis of Greedy Routing Algorithms on Arrays, Proc. 2nd Symposium on Parallel Algorithms and Architectures, pp. 2-10, ACM, 1990.
17. Leighton, T., F. Makedon, I. G. Tollis, A 2n - 2 Step Algorithm for Routing in an n x n Array with Constant Size Queues, Prof. Symposium on Parallel Algorithms and Architectures, pp. 328-335, ACM, 1989.
18. Ma, Y., S. Sen, D. Scherson, The Distance Bound for Sorting on Mesh Connected Processor Arrays is Tight, Proc. 21th Symposium on Foundations of Computer Science, pp. 255-263. IEEE, 1986.
19. Makedon, F., A. Simvonis, On Bit Serial Packet Routing for the Mesh and the Torus, Proc. 3rd Symposium on Frontiers of Massively Parallel Computation, pp. 294-302, IEEE, 1990.
20. Makedon, F., A. Simvonis, Multipacket Routing on Rings, Proc. 1st International ACPC Conference, LNCS 591, pp. 226-237, Springer-Verlag, Berlin, 1991.
21. Newman, I., A. Schuster, Hot Potato Worm Routing via Store-and-Forward Packet Routing, Journal oi Parallel and Distributed Computing, 30, 1995, 76-84.
22. Park, A., K. Balasubramanian, Reducing Communication Costs for Sorting on Mesh-Connected and Linearly Connected Parallel Computers, Journal of Parallel and Distributed Computing, 9, 1990, 318-322.
23. Rajasekaran, S., k-k Routing, k-k Sorting, and Cut-Through Routing on the Mesh, Journal of Algorithms, 19, 1995, 361-382.
24. Rajasekaran, S., M. Raghavachari, Optimal Randomized Algorithms for Multipacket and Cut Through Routing on the Mesh. Proc. 3rd Symposium on Parallel and Distributed Processing, IEEE, pp. 305-311, 1991.
25. Rajasekaran, S., Th. Tsantilas, Optimal Routing Algorithms for Mesh-Connected Processor Arrays, Algorithmica, 8, 1992, 21-38.
26. Reif, J., L. G. Valiant, A Logarithmic Time Sort for Linear Size Networks, Journal of the ACM, 34, 1987, 68-76.
27. Reischuk, R., Probabilistic Parallel Algorithms for Sorting and Selection, SIAM Journal on Computing, 14, 1985, 396-411.
28. Schnorr, C. P., A. Shamir, An Optimal Sorting Algorithm for Mesh Connected Computers, Proc. 18r/i Symposium on Theory of Computing, pp. 255-263, ACM, 1986.
29. Sibeyn, J. F., M. Kaufmann, Randomized k-k Sorting on Meshes, draft, 1992.
30. Thompson, C. D., H. T. Kung, Sorting on a Mesh Connected Parallel Computer, Communications of the ACM, 20, 1977, 263-270.
31. Valiant, L. G., A Bridging Model for Parallel Computation, Communications of the ACM, 33(8), 1990, 103-111.
32. Valiant, L. G., G. J. Brebner, Universal Schemes for Parallel Communication, Proc. 13th Symposium on Theory of Computing, pp. 263-277, ACM, 1981.