Title :
The NC equivalence of planar integer linear programming and Euclidean GCD
Author :
Shallcross, David ; Pan, Victor ; Lin-Kriz, Yu
Author_Institution :
Bellcore, Morristown, NJ, USA
Abstract :
We show NC-reduction of integer linear programming with two variables to the evaluation of the remainder sequence arising in the application of the Euclidean algorithm to two positive integers. Due to the previous result of X. Deng (1989), this implies NC-equivalence of both of these problems, whose membership in NC, as well as P-completeness, remain unresolved open problems
Keywords :
computational complexity; computational geometry; integer programming; linear programming; Euclidean GCD; Euclidean algorithm; NC equivalence; NC-reduction; P-completeness; planar integer linear programming; positive integers; remainder sequence; Cities and towns; Computational complexity; Computer science; Concurrent computing; Educational institutions; Equations; Integer linear programming; Lattices; Mathematics; Polynomials;
Conference_Titel :
Foundations of Computer Science, 1993. Proceedings., 34th Annual Symposium on
Conference_Location :
Palo Alto, CA
Print_ISBN :
0-8186-4370-6
DOI :
10.1109/SFCS.1993.366831
