Synopsis
How to make a given spanning tree optimal through inverse optimization
A clear look at how researchers define and solve inverse optimization problems, focusing on minimum spanning trees. It explains why perturbing cost data can turn a chosen tree into the optimal one under a new cost vector.
In this work, the authors study the inverse spanning tree problem in undirected graphs and show how it connects to assignment and transportation problems. The discussion covers dual formulations, algorithmic strategies, and how these methods achieve efficiency in practice.
- Foundations of inverse optimization and why small data changes can guarantee optimality.
- Transformations that convert the problem into well-known formats like assignment, minimum cost flow, and transportation problems.
- Algorithmic approaches, including shortest-path methods and cost-scaling techniques, with time analyses.
- Duality concepts and how primal-dual relationships guide finding the best perturbations.
Ideal for readers of operations research, optimization, and algorithm design who want a concrete treatment of inverse problems and spanning trees.
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