Diameter Minimization by Shortcutting with Degree Constraints
Abstract
We consider the problem of adding a fixed number of new edges to an undirected graph in order to minimize the diameter of the augmented graph, and under the constraint that the number of edges added for each vertex is bounded by an integer. The problem is motivated by networkdesign applications, where we want to minimize the worst case communication in the network without excessively increasing the degree of any single vertex, so as to avoid additional overload. We present three algorithms for this task, each with their own merits. The special case of a matching augmentation, when every vertex can be incident to at most one new edge, is of particular interest, for which we show an inapproximability result, and provide bounds on the smallest achievable diameter when these edges are added to a path. Finally, we empirically evaluate and compare our algorithms on several reallife networks of varying types.
 Publication:

arXiv eprints
 Pub Date:
 September 2022
 DOI:
 10.48550/arXiv.2209.00370
 arXiv:
 arXiv:2209.00370
 Bibcode:
 2022arXiv220900370A
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Social and Information Networks
 EPrint:
 A shorter version of this work has been accepted at the IEEE ICDM 2022 conference