| Framework | For two sets 8 and T, let P be the set of un-ordered pairs {u, v} where u E S and v E T. Our focus is on the following dispersion functions: the sum measure hs(S, T) = vakp d(u,v), the spanning tree measure ht(S, T) given by the cost of the minimum spanning tree of the set S UT, and the min measure hm(S, T) = minmvkp d(u, 2)). |
| Framework | To prove (ii) let T be the tree obtained by adding all points of O \ S directly to their respective closest points on the minimum spanning tree of S. T is a spanning tree , and hence a Steiner tree, for the points in set S U 0. |
| Framework | The proof follows by noting that we get a spanning tree by connecting each u,- to its closest point in Si_1. |
| Introduction | We consider three natural dispersion functions on the sentences in a summary: sum of all-pair sentence dissimilarities, the weight of the minimum spanning tree on the sentences, and the minimum of all-pair sentence dissimilarities. |