Shortest Paths along a Sequence of Line Segments in Euclidean Spaces

Nguyen Ngoc Hai; Phan Thanh An; Phong Thi Thu Huyen

Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

Shortest paths
ordered paths
shortest ordered paths
straightest paths
concatenation of paths

Mathematics Subject Classification

65K10, 52B05, 52B55, 51M20

Suggested citation

N. N. Hai, P. T. An, P. T. T. Huyen. “Shortest Paths along a Sequence of Line Segments in Euclidean Spaces.” Journal of Convex Analysis 26 (2019), No. 4, 1089–1112.