Exact algorithms for minimum routing cost trees

Given a set of points and distances between them, a basic problem in network design calls for selecting a graph connecting them at minimum total {\em routing cost}, i.e., the sum over all pairs of points of the length of their shortest path in the graph. In this paper we describe some branch and bound algorithms for the exact solution of a relevant special case arising when the graph has to be a tree. One of the enhancements to our algorithms is the use of ``LP shortcutting'', which we introduce as a general purpose technique for speeding up the search. Besides network design, we show how trees of small routing cost find useful application in computational biology, where they can be used to determine good alignments of genomic sequences. This leads to a novel alignment heuristic that we analyze in our computational section.