One line and n points

: 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 2. We obtain a tight O(log2 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, and we prove a tight (n) bound for its expected runtime. ? 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 453?471, 2003

• Type: Conference
• Year: 2001
• Where: STOC
• Authors: Bernd Gärtner, József Solymosi, Falk Tschirschnitz, Emo Welzl, Pavel Valtr
• Keywords: Algorithms, Certain 2-variable Linear, RANDOM-EDGE Simplex Algorithm, Randomized Pivoting Process, STOC 2001