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Mathematics of Operations Research
A caterpillar network (or graph) G is a tree with the property that removal of the leaf edges of Gleaves one with a path. Here we focus on minimum weight spanning caterpillars where the vertices are points in the Euclidean plane and the costs of the path edges and the leaf edges are multiples of their corresponding Euclidean lengths. The flexibility in choosing the weight for path edges versus the weight for leaf edges gives some useful flexibility in modeling. In particular, one can accommodate problems motivated by communications theory such as the “last mile problem.” Geometric and probabilistic inequalities are developed that lead to a limit theorem that is analogous to the well-known Beardwood, Halton, and Hammersley theorem for the length of the shortest tour through a random sample, but the minimal spanning caterpillars fall outside the scope of the theory of subadditive Euclidean functionals.
Euclidean networks, subadditive Euclidean functional, caterpillar graphs, shortest paths, traveling salesman problem, Beardwood, Halton, and Hammersley theorem, minimal spanning trees, Gutman graphs
Jevtić, P., & Steele, J. (2015). Euclidean Networks with a Backbone and a Limit Theorem for Minimum Spanning Caterpillars. Mathematics of Operations Research, 40 (4), 992-1004. http://dx.doi.org/10.1287/moor.2014.0706
Date Posted: 27 November 2017
This document has been peer reviewed.