Voronoi Diagrams in Facility Location

Sugihara, Kokichi

doi:10.1007/978-0-387-74759-0_707

Kokichi Sugihara³

434 Accesses

Article Outline

Keywords

Facility Location Problems

Voronoi Diagrams

Farthest-Point Voronoi Diagram

Variations in the Distance

Multiple-Facility Location

Concluding Remarks

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 2,500.00; Price excludes VAT (USA)

Hardcover Book: USD 2,499.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

Aurenhammer F (1991) Voronoi diagram: A survey of a fundamental geometric data structure. ACM Computing Surveys 23:345–405
Article Google Scholar
Edelsbrunner H (1987) Algorithms in combinatorial geometry. Springer, Berlin
MATH Google Scholar
Fortune S (1987) A sweepline algorithm for Voronoi diagrams. Algorithmica 2:153–174
Article MATH MathSciNet Google Scholar
Iri M, Murota K, Ohya T (1984) A fast Voronoi diagram algorithm with applications to geographical optimization problems. In: Thoft-Christensen P (ed) Proc. IFIP Conf. System Modelling and Optimization (1983, Copenhagen), Lecture Notes Control Inform Sci. Springer, Berlin, 273–288
Google Scholar
Kubota K, Iri M (1991) Estimates of rounding errors with fast automatic differentiation and interval analysis. J Inform Process 14:508–515
MATH MathSciNet Google Scholar
Ohya T, Iri M, Murota K (1984) Improvements of the incremental method for the Voronoi diagram with computational comparison of various algorithms. J Oper Res Soc Japan 27:306–336
MATH MathSciNet Google Scholar
Okabe A, Boots B, Sugihara K, Chui SN (2000) Spatial tessellations: Concepts and applications of Voronoi diagrams. Wiley, New York
MATH Google Scholar
Okabe A, Suzuki A (1987) Stability of spatial competition for a large number of firms on a bounded two-dimensional space. Environm Plan A 19:1067–1082
Article Google Scholar
Okabe A, Suzuki A (1997) Locational optimization problems solved through Voronoi diagrams. Europ J Oper Res 98:445–456
Article MATH Google Scholar
Preparata FP, Shamos MI (1985) Computational geometry: An introduction. Springer, Berlin
Google Scholar
Sugihara K, Iri M (1994) A robust topology-oriented incremental algorithm for Voronoi diagrams. Internat J Comput Geom Appl 4:179–228
Article MATH MathSciNet Google Scholar
Suzuki A, Drezner Z (1996) ‘The p-center location problem in an area. Location Sci 4:69–82
Article MATH Google Scholar

Download references

Author information

Authors and Affiliations

Department Math. Engineering and Information Physics, Graduate School of Engineering University Tokyo, Tokyo, Japan
Kokichi Sugihara

Authors

Kokichi Sugihara
View author publications
You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA
Christodoulos A. Floudas
Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA
Panos M. Pardalos

Rights and permissions

Reprints and permissions

Copyright information

About this entry

Cite this entry

Sugihara, K. (2008). Voronoi Diagrams in Facility Location . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_707

Download citation

DOI: https://doi.org/10.1007/978-0-387-74759-0_707
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-74758-3
Online ISBN: 978-0-387-74759-0
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering

Publish with us

Policies and ethics