Tight bounds on the size of fault-tolerant merging and sorting networks with destructive faults

SIAM Journal on Computing

Volumn 29, Issue 1, 1999, Pages 258-273

  Leighton, Tom ^a   Ma, Yuan ^a,b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPARATOR CIRCUITS; ELECTRIC NETWORK ANALYSIS; ELECTRIC NETWORK SYNTHESIS; MATHEMATICAL MODELS; MERGING; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; SORTING;

FAULT TOLERANT MERGING-SORTING NETWORKS; PROBABILISTIC ANALYSIS OF ALGORITHMS;

ALGORITHMS;

EID: 0342733653     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539796305298     Document Type: Article

References (25)

1. M. AJTAI, J. KOMLÓS, AND E. SZEMERÉDI, An O(n log n) sorting network, in Proc. 15th ACM Symposium on Theory of Computing, Boston, MA, 1983, pp. 1-9.
2. S. ASSAF AND E. UPFAL, Fault-tolerant sorting network, in Proc. 31st IEEE Symposium on Foundations of Computer Science, St. Louis, MO, 1990, pp. 275-284.
3. K. E. BATCHER, Sorting networks and their applications, in Proc. AFIPS Spring Joint Computer Conference, 32, Atlantic City, NJ, 1968, pp. 307-314.
4. P. DONEJKO, K. DIKS, A. PELC, AND M. PIOTRÓW, Reliable minimum finding comparator networks, in Proc. 19th Symposium on Mathematical Foundations of Computer Science, I. Prívara, B. Rovan, and P. Ružička, eds., Košice, Slovakia, 1994, Lecture Notes in Comput. Sci. 841, Springer-Verlag, Berlin, 1994, pp. 306-315.
5. D. KLEITMAN, T. LEIGHTON, AND Y. MA, On the design of Boolean circuits that contain partially unreliable gates, in Proc. 35th IEEE Symposium on Foundations of Computer Science, Santa Fe, NM, 1994, pp. 332-346.
6. D. E. KNUTH, The Art of Computer Programming, Volume 3: Sorting and Searching, Addison-Wesley, Reading, MA, 1973.
7. S.-Y. KUO AND S.-C. LIANG, Defect-tolerant hierarchical sorting networks for wafer-scale integration, IEEE J. Solid-State Circuits, 26 (1991), pp. 1212-1222.
8. T. LEIGHTON, Tight bounds on the complexity of parallel sorting, IEEE Trans. Comput., C-34 (1985), pp. 326-335.
9. T. LEIGHTON, Introduction to Parallel Algorithms and Architectures: Arrays, Trees, and Hypercubes, Morgan-Kaufmann, San Mateo, CA, 1992.
10. 2 n) barrier for sorting with faults. J. Comput. System Sci., 54 (1997), pp. 265-304.
11. T. LEIGHTON, Y. MA, AND C. G. PLAXTON, Highly fault-tolerant sorting circuits, in Proc. 32nd IEEE Symposium on Foundations of Computer Science, San Juan, Puerto Rico, 1991, pp. 458-469.
12. Y. MA, Fault-Tolerant Sorting Networks, Ph.D. thesis, MIT. Cambridge, MA, 1994.
13. Y. MA, An O(n log n)-size fault-tolerant sorting network, in Proc. 28th ACM Symposium on the Theory of Computing, Philadelphia, PA, 1996, pp. 266-275.
14. M. PIOTRÓW, Depth optimal sorting networks resistant to k passive faults, in Proc. 7th ACM-SIAM Symposium on Discrete Algorithms, Atlanta, GA, 1996, pp. 242-251.
15. N. PIPPENGER, On networks of noisy gates, in Proc. 26th IEEE Symposium on Foundations of Computer Science, 1985, pp. 30-36.
16. L. RUDOLPH, A robust sorting network, IEEE Trans. Comput., 34 (1985), pp. 344-354.
17. M. R. SAMATHAM AND D. K. PRADHAN, The De Bruijn multiprocessor network: A versatile parallel processing and sorting network for VLSI, IEEE Trans. Comput., 38 (1989), pp. 567-581.
18. M. SCHIMMLER AND C. STARKE, A correction network for N-sorters, SIAM J. Comput., 18 (1989), pp. 1179-1187.
19. J. SUN, E. CERNY, AND J. GECSEI, Design of a fault-tolerant sorting network, in Proc. Canadian Conference on Very Large Scale Integration, Ottawa, Canada, 1989, pp. 235-242.
20. J. SUN, E. CERNY, AND J. GECSEI, Sorting networks without critical stages, in Proc. Canadian Conference on Very Large Scale Integration, Montreal, Canada, 1990, pp. 5.4/1-8.
21. J. SUN, E. CERNY, AND J. GECSEI, Fault tolerance in a class of sorting networks, IEEE Trans. Comput., 43 (1994), pp. 827-837.
22. J. SUN AND J. GECSEI, A multiple-fault tolerant sorting network, in Proc. 21st International Symposium on Fault-Tolerant Computing, Montreal, Canada, IEEE Computer Society Press, Los Alamitos, CA, 1991, pp. 274-281.
23. J. SUN, J. GECSEI, AND E. CERNY, An improvement in robust sorting networks, in Proc. 23rd ASILOMAR Conference on Signals, Systems and Computers, Pacific Grove, CA, 1989, pp. 1036-1040.
24. J. SUN, J. GECSEI, AND E. CERNY, Fault-tolerance in balanced sorting networks, J. Electronic Testing Theory Appl., 1 (1990), pp. 31-41.
25. A. C. YAO AND F. F. YAO, On fault-tolerant, networks for sorting, SIAM J. Comput., 14 (1985), pp. 120-128.