Finding the ?-core of a tree
An ?-core of a tree T=(V,E) with |V|=n, is a path P with length at most ? that is central with respect to the property of minimizing the sum of the distances from the vertices in P to all the vertices of T not in P. The distance between two vertices is the length of the shortest path joining them. In this paper we present efficient algorithms for finding the ?-core of a tree. For unweighted trees we present an O(n?) time algorithm, while for weighted trees we give a procedure with time complexity of . The algorithms use two different types of recursive principle in their operation.
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