Combinatorial algorithms for solving the restricted bounded inverse optimal value problem on minimum spanning tree under weighted l(8) norm

We consider the restricted bounded inverse optimal value problem on minimum spanning tree. In a connected undirected network G = (V , E , w), we are given a spanning tree T-0 , a weight vector w , a lower bound vector l , an upper bound vector u , a cost vector c and a value K. We aim to obtain a new weight vector (w) over bar satisfying the lower and upper bounds such that T-0 is a minimum spanning tree under the vector (w) over bar with weight K. We aim to minimize the modification cost max(ei & ISIN;E) c(i)|(w) over bar(i) -w(i)| under weighted l(& INFIN;) norm. We first analyze some properties of feasible and optimal solutions of the problem and develop a strongly polynomial time algorithm with running time O(m(2)n), where m = |E| , n = |V|. Then we reduce the time complexity to O(m(2) log n) by devising a more complex algorithm using a binary search method. Thirdly, we apply the first algorithm to the problem under unit l(& INFIN;) norm, where c(i) = 1, and obtain an O(mn) time algorithm. Finally, we give some examples to demonstrate the algorithms and present some numerical experiments to show the effectiveness of these algorithms. (c) 2022 Elsevier B.V. All rights reserved.