On Minimum Average Stretch Spanning Trees in Polygonal 2-Trees

Abstract

AbstractA spanning tree of an unweighted graph is a minimum average stretch spanning tree if it minimizes the ratio of sum of the distances in the tree between the end vertices of the graph edges and the number of graph edges. We consider the problem of computing a minimum average stretch spanning tree in polygonal 2-trees, a super class of 2-connected outerplanar graphs. For a polygonal 2-tree on n vertices, we present an algorithm to compute a minimum average stretch spanning tree in O(n logn) time. This also finds a minimum fundamental cycle basis in polygonal 2-trees.KeywordsOuterplanar GraphExternal EdgeFundamental CycleUnweighted GraphAverage StretchThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.