Orienting Graphs to Optimize Reachability
Data Structures and Algorithms
2015-06-02 v1 Discrete Mathematics
Abstract
The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to minimize the number of such pairs. The paper describes a quadratic-time algorithm for the first problem, and a proof that the second problem is NP-hard to approximate within some constant 1+epsilon > 1. The latter proof also shows that the second problem is equivalent to ``comparability graph completion''; neither problem was previously known to be NP-hard.
Cite
@article{arxiv.cs/0205042,
title = {Orienting Graphs to Optimize Reachability},
author = {S. L. Hakimi and E. Schmeichel and Neal E. Young},
journal= {arXiv preprint arXiv:cs/0205042},
year = {2015}
}