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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Bibliographic Details
Published in:SIAM journal on computing Vol. 27; no. 4; pp. 960 - 971
Main Authors: Shallcross, D. F., Pan, V. Y., Lin-Kriz, Y.
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.08.1998
Subjects:
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
Integer programming
Linear programming
Parallel algorithms
Computational complexity
Algorithm complexity
Program complexity
ISSN:0097-5397, 1095-7111
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0097-5397
1095-7111
DOI:10.1137/S0097539794276841