text: A linear-time simplification of an algorithm of this type was developed by Emo Welzl for finding the smallest enclosing circle for a set of points on a two-dimensional plane.
full_question: A linear-time simplification of an algorithm of this type was developed by Emo Welzl for finding the smallest enclosing circle for a set of points on a two-dimensional plane. Although the set-cover problem is NP-complete, by defining indicator variables for each set one can obtain a fast 2-approximation algorithm that utilizes a technique of this type. Leonid Khachiyan was the first to show that this method admits a polynomial-time algorithm by the application of the ellipsoid method. A commonly-used algorithm in this class of methods constructs a polytope of solutions and walks along strictly-decreasing edges until it obtains a solution; that is Dantzig's simplex algorithm. For 10 points, name these techniques which optimize objective functions of the namesame form.
first_sentence: A linear-time simplification of an algorithm of this type was developed by Emo Welzl for finding the smallest enclosing circle for a set of points on a two-dimensional plane.
raw_answer: linear programming [or LP; or linear optimization; prompt on "optimization"]