A distance function for computing on finite subsets of Euclidean spaces

作者：Ghahremani Gol Hajar; Didehvar Farzad^*; Razavi Asadollah

来源：Acta Mathematicae Applicatae Sinica-English Series, 2018, 34(1): 197-208.

DOI：10.1007/s10255-018-0735-0

• geodesic
• least square method
• vehicle routing problem
• traveling salesman problem
• three dimensional triangulation

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.

• 出版日期2018-1