Solution Methodologies for the Smallest Enclosing Circle Problem

Authors:
Sheng Xu;Robert M. Freund;Jie Sun
Affiliations:
Gintic Institute of Manufacturing Technology, Singapore. sxu@gintic.gov.sg;Sloan School of Management, Massachusetts Institute of Technology and Singapore-MIT Alliance. rfreund@mit.edu;Department of Decision Sciences, National University of Singapore and Singapore-MIT Alliance. jsun@nus.edu.sg
Venue:
Computational Optimization and Applications
Year:
2003

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Abstract

Given a set of circles C = {c1, …, cn} on the Euclidean plane with centers {(a1, b1), …, (an, bn)} and radii {r1, …, rn}, the smallest enclosing circle (of fixed circles) problem is to find the circle of minimum radius that encloses all circles in C. We survey four known approaches for this problem, including a second order cone reformulation, a subgradient approach, a quadratic programming scheme, and a randomized incremental algorithm. For the last algorithm we also give some implementation details. It turns out the quadratic programming scheme outperforms the other three in our computational experiment.