Making Bidirected Graphs Strongly Connected

TL;DR

This paper addresses the problem of transforming bidirected graphs into strongly connected graphs efficiently, providing optimal solutions for adding signs and near-optimal solutions for adding arcs with linear-time algorithms.

Contribution

It introduces linear-time algorithms for making bidirected graphs strongly connected by adding signs optimally and arcs near-optimally, improving computational efficiency.

Findings

Minimum number of signs needed for strong connectivity identified

Linear-time algorithm for optimal sign addition developed

Linear-time algorithm for near-optimal arc addition provided

Abstract

We consider problems to make a given bidirected graph strongly connected with minimum cardinality of additional signs or additional arcs. For the former problem, we show the minimum number of additional signs and give a linear-time algorithm for finding an optimal solution. For the latter problem, we give a linear-time algorithm for finding a feasible solution whose size is equal to the obvious lower bound or more than that by one.