# Linear-time algorithms for linear programming in R3 and related problems

@article{Megiddo1982LineartimeAF, title={Linear-time algorithms for linear programming in R3 and related problems}, author={Nimrod Megiddo}, journal={23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)}, year={1982}, pages={329-338} }

Linear-time for Linear Programming in R2 and R3 are presented. The methods used are applicable for some other problems. For example, a linear-time algorithm is given for the classical problem of finding the smallest circle enclosing n given points in the plane. This disproves a conjecture by Shamos and Hoey that this problem requires Ω(n log n) time. An immediate consequence of the main result is that the problem of linear separability is solvable in linear-time. This corrects an error in…

## 679 Citations

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