On the Computational Complexity of Optimal Sorting Network Verification
A sorting network is a combinational circuit for sorting, constructed from comparison-swap units. The depth of such a circuit is a measure of its running time. It is reasonable to hypothesize that only the fastest (that is, the shallowest) networks are likely to be fabricated. It is shown that the problem of verifying that a given sorting network actually sorts is Co-NP complete even for sorting networks of depth only 4 [log n] + O(1) greater than optimal. This is shallower than previous depth bounds by a factor of two.
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- M. Ajtai, J. Komlós, and E. Szemerédi. An O(n. log n) sorting network. Proc. 15th Ann. ACM Symp. on Theory of Computing, pages 1–9, April 1983.Google Scholar
- K. E. Batcher. Sorting networks and their applications. In Proc. AFIPS Spring Joint Computer Conference, volume 32, pages 307–314, April 1968.Google Scholar
- M. Chung and B. Ravikumar. On the size of test sets for sorting and related problems. In Proc. 1987 International Conference on Parallel Processing. Penn State Press, August 1987.Google Scholar
- R. L. Drysdale. Sorting networks which generalize batcher’s odd-even merge. Honors Paper, Knox College, May 1973.Google Scholar
- R. W. Floyd and D. E. Knuth. Improved constructions for the Bose-Nelson sorting problem (preliminary report). Notices of the AMS, 14: 283, 1967.Google Scholar
- M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979.Google Scholar
- D. E. Knuth. Sorting and Searching, volume 3 of The Art of Computer Programming. Addison-Wesley, 1973.Google Scholar
- I. Parberry. The alternating sorting network. Technical Report CS-87–26, Dept. of Computer Science, Penn. State Univ., September 1987.Google Scholar
- I. Parberry. Sorting networks. Technical Report CS-88–08, Dept. of Computer Science, Penn. State Univ., March 1988.Google Scholar
- I. Parberry. A computer-assisted optimal depth lower bound for sorting networks with nine inputs. In Proceedings of Supercomputing ‘89, pages 152–161, 1989.Google Scholar
- T. J. Schaefer. The complexity of satisfiability problems. In Proc. 10th Annual ACM Symposium on Theory of Computing, pages 216–226. Association for Computing Machinery, 1978.Google Scholar
- D. C. Van Voorhis. An economical construction for sorting networks. In Proc. AFIPS National Computer Conference, volume 43, pages 921–926, 1974.Google Scholar