Combinatorial algorithms for restricted inverse optimal value problems on minimum spanning tree under weighted 1 1 norm

We study the restricted inverse optimal value problem on minimum spanning tree under weighted.. 1 norm. In a connected edge-weighted network..(..,..,..), we are given a spanning tree...., a cost vector.. and a value... We aim to obtain a new weight vector.. satisfying the bounded constraint such that.... is a minimum spanning tree under.. whose weight is just... We focus on minimizing the modification cost under weighted.... norm. We first convert its mathematical model into a linear programming problem (..). Then we solve its dual problem (..) by a sub-problem (....*) corresponding to the critical value..* which can be calculated by a binary search method. Impressively the sub-problem.... for... R can be transformed into a minimum cost flow problem on an auxiliary network. Finally, we propose an.. (|.. |2|.. |2 log |.. | log(|.. |........)) algorithm, where........ is the maximum cost of the vector...