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A distance function for computing on finite subsets of Euclidean spaces

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Abstract

In practical purposes for some geometrical problems, specially the fields in common with computer science, we deal with information of some finite number of points. The problem often arises here is: “How are we able to define a plausible distance function on a finite three dimensional space?” In this paper, we define such a distance function in order to apply it to further purposes, e.g. in the field settings of transportation theory and geometry. More precisely, we present a new model for traveling salesman problem and vehicle routing problem for two dimensional manifolds in three dimensional Euclidean space, the second problem on which we focus on this line is, three dimensional triangulation.

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Acknowledgements

The authors would like to thank the anonymous referees for their careful reading of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Shahed University, Tehran, 3319118651, Iran

    Hajar Ghahremani-Gol

  2. Department of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Av, Tehran, 1591634311, Iran

    Hajar Ghahremani-Gol, Farzad Didehvar & Asadollah Razavi

  3. Department Pure Mathematics, Faculty of Mathematics and Computer Science, Shahid Bahonar University of Kerman, Kerman, Iran

    Asadollah Razavi

Authors
  1. Hajar Ghahremani-Gol
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  2. Farzad Didehvar
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  3. Asadollah Razavi
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Correspondence to Farzad Didehvar.

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Ghahremani-Gol, H., Didehvar, F. & Razavi, A. A distance function for computing on finite subsets of Euclidean spaces. Acta Math. Appl. Sin. Engl. Ser. 34, 197–208 (2018). https://doi.org/10.1007/s10255-018-0735-0

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  • DOI: https://doi.org/10.1007/s10255-018-0735-0

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