Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given a solution x* and an a priori estimated cost vector c, the inverse optimization problem is to identify another cost vector d so that x* is optimal with respect to the cost vector d and its deviation from c is minimum. ,  consider the inverse spanning tree problem on an undirected graph G = (N, A) with n nodes and m arcs, and where the deviation beten c and d is defined by the rectilinear distance beten the two vectors, that is, L1 norm.  show that the inverse spanning tree problem can be formulated as the dual of an assignment problem on a bipartite network G0 = (N0, A0) with [math not displayed] and [math not displayed]. The bipartite ne twork satisfies the property that |N1| = (n - 1), |N2| = (m - n + 1), and |A0| = O(nm). In general, |N1| << |N2|. Using this special structure of the assignment problem,  develop a specific implementation of the successive shortest path algorithm that runs in O(n3) time.  also consider the ighted version of the inverse spanning tree problem in which the objective function is to minimize the sum of the ighted deviations of arcs. The ighted inverse spanning tree can be formulated as the dual of the transportation problem. Using a cost scaling algorithm, this transportation problem can be solved in O(n2m log(nC)) time, where C denotes the largest arc cost in the data. Finally,  consider a minimax version of the inverse spanning tree problem and show that it can be solved in O(n2) time.
['P. T. Sokkalingam', 'Ravindra K. Ahuja', 'James B. Orlin']
I am writing a research paper on a idea Solving Inverse Spanning Tree Problems Through Network Flow Techniques
[{"from": "human", "value": "I am writing a research paper on a idea Solving Inverse Spanning Tree Problems Through Network Flow Techniques"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given a solution x* and an a priori estimated cost vector c, the inverse optimization problem is to identify another cost vector d so that x* is optimal with respect to the cost vector d and its deviation from c is minimum. ,  consider the inverse spanning tree problem on an undirected graph G = (N, A) with n nodes and m arcs, and where the deviation beten c and d is defined by the rectilinear distance beten the two vectors, that is, L1 norm.  show that the inverse spanning tree problem can be formulated as the dual of an assignment problem on a bipartite network G0 = (N0, A0) with [math not displayed] and [math not displayed]. The bipartite ne twork satisfies the property that |N1| = (n - 1), |N2| = (m - n + 1), and |A0| = O(nm). In general, |N1| << |N2|. Using this special structure of the assignment problem,  develop a specific implementation of the successive shortest path algorithm that runs in O(n3) time.  also consider the ighted version of the inverse spanning tree problem in which the objective function is to minimize the sum of the ighted deviations of arcs. The ighted inverse spanning tree can be formulated as the dual of the transportation problem. Using a cost scaling algorithm, this transportation problem can be solved in O(n2m log(nC)) time, where C denotes the largest arc cost in the data. Finally,  consider a minimax version of the inverse spanning tree problem and show that it can be solved in O(n2) time."}]