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One line and n points
2003
Random structures & algorithms (Print)
We analyze a randomized pivoting process involving one line and n points in the plane. The process models the behavior of the RANDOM-EDGE simplex algorithm on simple polytopes with n facets in dimension n Ϫ 2. We obtain a tight O(log 2 n) bound for the expected number of pivot steps. This is the first nontrivial bound for RANDOM-EDGE, which goes beyond bounds for specific polytopes. The process itself can be interpreted as a simple algorithm for certain 2-variable linear programming problems,
doi:10.1002/rsa.10099
fatcat:dotejrveuvbo7p44cbaoogzupi