Geometric Applications of a Randomized Optimization Technique (1999)
| Venue: | Discrete Comput. Geom |
| Citations: | 45 - 6 self |
BibTeX
@ARTICLE{Chan99geometricapplications,
author = {Timothy M. Chan},
title = {Geometric Applications of a Randomized Optimization Technique},
journal = {Discrete Comput. Geom},
year = {1999},
volume = {22},
pages = {547--567}
}
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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 1centers, and solving linear programs with k violations. 1 Introduction Consider the classic randomized algorithm for finding the minimum of r numbers minfA[1]; : : : ; A[r]g: Algorithm rand-min 1. randomly pick a permutation hi 1 ; : : : ; i r i of h1; : : : ; ri 2. t /1 3. for k = 1; : : : ; r do 4. if A[i k ] ! t then 5. t / A[i k ] 6. return t By a well-known fact [27, 44], the expected number of times that step 5 is execut...
