Planar Integer Linear Programming is NC Equivalent to Euclidean GCD
It is not known if planar integer linear programming is P-complete or if it is in NC, and the same can be said about the computation of the remainder sequence of the Euclidean algorithm applied to two integers. However, both computations are NC equivalent. The latter computational problem was reduce...
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| Veröffentlicht in: | SIAM journal on computing Jg. 27; H. 4; S. 960 - 971 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Philadelphia, PA
Society for Industrial and Applied Mathematics
01.08.1998
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| ISSN: | 0097-5397, 1095-7111 |
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| Abstract | It is not known if planar integer linear programming is P-complete or if it is in NC, and the same can be said about the computation of the remainder sequence of the Euclidean algorithm applied to two integers. However, both computations are NC equivalent. The latter computational problem was reduced in NC to the former one by Deng [Mathematical Programming: Complexity and Application, Ph.D. dissertation, Stanford University, Stanford, CA, 1989; Proc. ACM Symp. on Parallel Algorithms and Architectures, 1989,pp. 110--116]. We now prove the converse NC-reduction. |
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| AbstractList | It is not known if planar integer linear programming is P-complete or if it is in NC, and the same can be said about the computation of the remainder sequence of the Euclidean algorithm applied to two integers. However, both computations are NC equivalent. The latter computational problem was reduced in NC to the former one by Deng [Mathematical Programming: Complexity and Application, Ph.D. dissertation, Stanford University, Stanford, CA, 1989; Proc. ACM Symp. on Parallel Algorithms and Architectures, 1989,pp. 110--116]. We now prove the converse NC-reduction. |
| Author | Pan, V. Y. Lin-Kriz, Y. Shallcross, D. F. |
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| Copyright | 1998 INIST-CNRS [Copyright] © 1998 Society for Industrial and Applied Mathematics |
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| Snippet | It is not known if planar integer linear programming is P-complete or if it is in NC, and the same can be said about the computation of the remainder sequence... |
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| SubjectTerms | Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Computer science Computer science; control theory; systems Exact sciences and technology Integer programming Linear algebra Linear programming Mathematical programming Operational research and scientific management Operational research. Management science Theoretical computing |
| Title | Planar Integer Linear Programming is NC Equivalent to Euclidean GCD |
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