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A Wavefront Approach to Center Location Problems with Barriers

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Abstract

Center location problems have many applications, for example, in the public sector, and various different algorithms have been developed for their solution. This paper suggests a novel solution strategy to the problem that is based on the propagation of circular wavefronts. The approach is discussed theoretically and implemented both as a physical experiment and as a computer simulation.

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References

  • Ben-Moshe, B., M.J. Katz, and J.S.B. Mitchell. (2001). “Farthest Neighbors and Center Points in the Presence of Rectangular Obstacles.” In Proc. 17th ACM Symposium on Computational Geometry.

  • Brady, S.D. and R. Rosenthal. (1980). “Interactive Computer Graphical Solutions to Constrained Minimax Location Problems.” AIIE Transactions 241–248.

  • Brady, S.D. and R. Rosenthal. (1983). “Interactive Graphical Minimax Location of Multiple Facilities with General Constraints.” IIE Transactions 15, 242–252.

    Google Scholar 

  • Chew, L.P. and R.L. Drysdale. (1985). “Voronoi Diagrams Based on Convex Distance Functions.” In Proceeding of the ACM Symposium on Computational Geometry. Baltimore, MD, pp. 235–244.

  • Choi, J., C.-S. Shin, and S.K. Kim. (1998). “Computing Weighted Rectilinear Median and Center Set in the Presence of Obstacles.” In Proc. 9th Annu. Internat. Sympos. Algorithms Comput., Vol. 1533 of Lecture Notes in Computer Science. Springer-Verlag, pp. 29–38.

  • Dearing, P.M. and R. Segars Jr. (2002a). “An Equivalence Result for Single Facility Planar Location Problems with Rectilinear Distance and Barriers.” Annals of Operations Research 111, 89–110.

    Article  Google Scholar 

  • Dearing, P.M. and R. Segars Jr. (2002b). “Solving Rectilinear Planar Location Problems with Barriers by a Polynomial Partitioning.” Annals of Operations Research 111, 111–133.

    Article  Google Scholar 

  • Dearing, P.M., H.W. Hamacher, and K. Klamroth. (2002). “Dominating Sets for Rectilinear Center Location Problems with Polyhedral Barriers.” Naval Research Logistics 49, 647–665.

    Article  Google Scholar 

  • Drezner, Z., K. Klamroth, A. Schöbel, and G.O. Wesolowsky. (2002). “The Weber Problem.” In Z. Drezner and H.W. Hamacher (eds.), Facility Location: Application, and Theory. New York: Springer-Verlag, pp. 1–36.

    Google Scholar 

  • Feynman, R.P., R.B. Leighton, and M. Sands. (1998). The Feynman Lectures on Physics, Vol. 1–3. Addison Wesley.

  • Francis, R.L. (1967). “Some Aspects of a Minimax Location Problem.” Operations Research 15, 1163–1169.

    Article  Google Scholar 

  • Gamito, M. and F. Musgrave. (2002). “An Accurate Model for Wave Refraction Over Shallow Water.” Computers & Graphics 26, 291–307.

    Article  Google Scholar 

  • Hansen, P., B. Jaumard, and H. Tuy. (1995). “Global Optimization in Location.” In Z. Drezner (ed.), Facility Location. Springer Series in Operations Research, pp. 43–68.

  • Hershberger, J. and S. Suri. (1999). “An Optimal Algorithm for Euclidean Shortest Paths in the Plane.” SIAM Journal on Computing 28, 2215–2256.

    Article  Google Scholar 

  • Klamroth, K. (2001). “A Reduction Result for Location Problems with Polyhedral Barriers.” European Journal of Operational Research 130, 486–497.

    Article  Google Scholar 

  • Mitchell, J.S.B. (1992). “L 1 Shortest Paths Among Polygonal Obstacles in the Plane.” Algorithmica 8, 55–88.

    Article  Google Scholar 

  • Mitchell, J.S.B. (1998). “Geometric Shortest Paths and Network Optimization.” In J.-R. Sack and J. Urrutia, (eds.), Handbook of Computational Geometry. Elsevier Science.

  • Mitchell, J.S.B., G. Rote, and G. Woeginger. (1992). “Minimum-Link Paths Among Obstacles in the Plane.” Algorithmica 8, 431–459.

    Article  Google Scholar 

  • Segars Jr., R. (2000). “Location Problems with Barriers Using Rectilinear Distance.” Ph.D. thesis, Dept. of Mathematical Sciences, Clemson University, SC.

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Frießs, L., Klamroth, K. & Sprau, M. A Wavefront Approach to Center Location Problems with Barriers. Ann Oper Res 136, 35–48 (2005). https://doi.org/10.1007/s10479-005-2037-1

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