Two-best solutions under distance constraints: The model and exemplary results for matroids (Q1291060)

The authors investigate \(k\)-best questions with distance constraints \((k=2)\), deriving several results for valuated matroids. As a distance function on the set of all bases in a matroid the following function is taken: \(d(B_1, B_2)= {1\over 2}[\text{card}(B_1\setminus B_2)+ \text{card}(B_2\setminus B_1)]\). Two examples with maximum spanning trees in a medium size graph are discussed together with several ideas on \(k\)-best solutions.