Journal of Convex Analysis 26 (2019), No. 4, 1089--1112
Copyright Heldermann Verlag 2019
Shortest Paths along a Sequence of Line Segments in Euclidean Spaces
Nguyen Ngoc Hai
Department of Mathematics, International University, Vietnam National University, Ho Chi Minh City, Vietnam
nnhai@hcmiu.edu.vn
Phan Thanh An
Institute of Mathematics and Computer Science, University of Sao Paulo, Sao Carlos -- SP, Brasil
and: Institute of Mathematics, Vietnam Academy of Science and Technology, Cau Giay, Hanoi, Vietnam
thanhan@math.ac.vn
Phong Thi Thu Huyen
Institute of Mathematics, Vietnam Academy of Science and Technology, Cau Giay, Hanoi, Vietnam
ptthuyen@math.ac.vn
We present some analytical and geometric properties of shortest ordered paths joining two given points with respect to a sequence of line segments in a Euclidean space, especially their existence, uniqueness, characteristics, and conditions for concatenation of two shortest ordered paths to be a shortest ordered path. We then focus on straightest paths lying on a sequence of adjacent convex polygons in 2 or 3 dimensional spaces.
Keywords: Shortest paths, ordered paths, shortest ordered paths, straightest paths, concatenation of paths.
MSC: 65K10, 52B05, 52B55, 51M20.
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