One line and n points

Bernd Gärtner, Falk Tschirschnitz, Emo Welzl, József Solymosi, Pavel Valtr
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,
more » ... d we prove a tight ⌰(n) bound for its expected runtime.
doi:10.1002/rsa.10099 fatcat:dotejrveuvbo7p44cbaoogzupi