A linear-time algorithm to compute a MAD tree of an interval graph

A survey of the all-pairs shortest paths problem and its variants in graphs

“…In addition to average distance of a network, suppose if one is interested in designing a tree subnetwork of a given network such that the delay in sending a message between any two nodes of the network is minimum on the average, then such a tree can be modeled by finding the minimum average distance spanning tree (MAD) trees (MAD trees are also known as minimum routing cost spanning trees) [22]. Thus MAD trees also play an important role in communication networks [52].…”

“…In [21], an linear time algorithm is exhibited for computing a MAD tree of a given distance-hereditary graph. In [22] the average distance µ(G, w) of vertex-weighted graph (G, w) is defined as follows. If G is a graph with weight function w : V(G) → R + , then…”

“…where w(V) is the total weight of the vertices in G. Dahlhaus et al [22], show that for a given interval graph G a MAD tree can be computed in time O(m).…”