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Given an edge-weighted tree T, a trunk is a path P in T which minimizes the sum of the distances of all vertices in T from P plus the weight of path P. In this paper, we give efficient algorithms for finding a trunk of T. The first algorithm is a sequential algorithm which runs in O(n) time, where n is the number of vertices in T. The second algorithm is a parallel algorithm which runs in O(log n)...
A k-cluster of a tree includes a single path and k-1 sub-paths growing from that path. A k-MCore is a k-cluster that minimizes the sum of the distances of all vertices to the cluster plus the size of the cluster. This structure is motivated by the applications on overlay multicasting. The overlay multicast protocol constructs a virtual mesh spanning all member nodes of a multicast group. It employs...
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