The NC equivalence of planar integer linear programming and Euclidean GCD

D. Shallcross, V. Pan, Yu Lin-Kriz
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science  
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 Deng, this implies NC-equivalence of both of these problems, whose membership in NC, as well as P-completeness, remain unresolved open problems.
doi:10.1109/sfcs.1993.366831 dblp:conf/focs/ShallcrossPL93 fatcat:nfsmaqwgm5bb5cdazwa6af6s6a