Geometric Applications of a Randomized Optimization Technique

Abstract. We propose a simple, general, randomized technique to reduce certain geometric optimization problems to their corresponding decision problems. These reductions increase the expected time complexity by only a constant factor and eliminate extra logarithmic factors in previous, often more complicated, deterministic approaches (such as parametric searching). Faster algorithms are thus obtained for a variety of problems in computational geometry: finding minimal k-point subsets, matching point sets under translation, computing rectilinear p-centers and discrete 1-centers, and solving linear programs with k violations.

• Type: Conference
• Year: 1998
• Where: COMPGEOM
• Authors: Timothy M. Chan
• Keywords: COMPGEOM 1998, Corresponding Decision Problems, Discrete Geometry, Geometric Optimization Problems, Minimal K-point Subsets