2021/08/23 by Weiyi Ding, Ding, Weiyi, Xiaoxian Tang +1
Computer Science · Engineering · #14T90 #62R07 #68R01 #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #FOS: Mathematics #Numerical Methods and Algorithms #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2108.10124
openalex publication_date 2021/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the tropical projective torus, it is not guaranteed that the projection of a Fermat-Weber point of a given data set is a Fermat-Weber point of the projection of the data set. In this paper, we focus on the projection on the tropical triangle (the three-point tropical convex hull), and we develop one algorithm (Algorithm 1) and its improved version (Algorithm 4), such that for a given data set in the tropical projective torus, these algorithms output a tropical triangle, on which the projection of a Fermat-Weber point of the data set is a Fermat-Weber point of the projection of the data set. We implement these algorithms in R and test how it works with random data sets. The experimental results show that, these algorithms can succeed with a much higher probability than choosing the tropical triangle randomly, the succeed rate of these two algorithms is stable while data sets are changing randomly, and Algorithm 4 can output the results much faster than Algorithm 1 averagely.