Diameter Reduction via Arc Reversal

Abstract The diameter of a directed graph is the maximum distance between any pair of vertices. We study a problem that generalizes Oriented Diameter : For a given directed graph and a positive integer d , what is the minimum number of arc reversals required to obtain a graph with diameter at most d ? We investigate variants of this problem, considering the number of arc reversals and the target diameter as parameters. We show hardness results under certain parameter restrictions, and give polynomial time algorithms for planar and cactus graphs. This work is partly motivated by the relation between oriented diameter and the volume of directed edge polytopes, which we show to be independent.