Optimization and the geometry of numbers: packing and covering

Thomas Saaty
Joseph M. Katz Graduate School of Business
University of Pittsburgh
United States
Joyce M. Alexander
Counseling and Educational Psychology
School of Education
United States

Publication date: Jul, 1957

Journal: SIAM Review
Vol.: 17- Issue: 3- Pages: 475-519

Abstract: There are a number of useful applications gradually arising out of the geometry of numbers. In this paper we give a brief survey of the fields of packing and covering, stating some results, and giving illustrations of methods of proof and approaches to the subject. We then mention and discuss a variety of applications, summarizing results and occasionally providing proofs. Our hope is to focus attention on optimization problems not in the main stream of current optimization theories.

Keywords: Optimization, Packing, Covering, Survey