Inverse group 1-median problem on trees

Kien Trung Nguyen, ,Department of Mathematics, Teacher College, Can Tho University, Can Tho, Vietnam, Vo Nguyen Minh Hieu, Van Huy Pham, ,AI Lab, Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Vietnam
2017 Journal of Industrial and Management Optimization  
In location theory, group median generalizes the concepts of both median and center. We address in this paper the problem of modifying vertex weights of a tree at minimum total cost so that a prespecified vertex becomes a group 1-median with respect to the new weights. We call this problem the inverse group 1-median on trees. To solve the problem, we first reformulate the optimality criterion for a vertex being a group 1-median of the tree. Based on this result, we prove that the problem is N P
more » ... -hard. Particularly, the corresponding problem with exactly two groups is however solvable in O(n 2 log n) time, where n is the number of vertices in the tree. 2010 Mathematics Subject Classification. 90B10, 90B80, 90C27.
doi:10.3934/jimo.2019108 fatcat:hfik4zargfdapcfyxiuwtcs5qu