This book explores inverse spanning tree problems, a novel approach to measuring deviation from optimality. The author demonstrates how to formulate these problems as duals of assignment and transportation problems, opening up new avenues for efficient solutions. By presenting a detailed algorithm for the assignment problem and adapting cost scaling algorithms for transportation problems, the book provides practical methods for addressing inverse spanning tree problems in a range of time complexities. The author also examines weighted and minimax variations of the problem, expanding its applicability. Through these insights, this book not only contributes to the field of network optimization but also sheds light on the broader concept of deviation from optimality, making it a valuable resource for researchers and practitioners alike.
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