RIMS-1826 Approximation Algorithms for the Minimum 2-edge Connected Spanning Subgraph Problem and the Graph-TSP in Regular Bipartite Graphs via Restricted 2-factors By

In this paper, we address the minimum 2-edge connected spanning subgraph problem and the graph-TSP in regular bipartite graphs. For these problems, we present new approximation algorithms, each of which finds a restricted 2-factor close to a Hamilton cycle in the first step. We first prove that every regular bipartite graph of degree at least three has a square-free 2-factor. This immediately leads to 4/3-approximation algorithms for the minimum 2-edge connected spanning subgraph problem and the graph-TSP in regular bipartite graphs. We then design a 7/6-approximation algorithm for the minimum 2-edge connected spanning subgraph problem in 3-edge connected cubic bipartite graphs, which begins with a 2-factor intersecting all 3and 4-edge cuts. This improves upon the previous best ratio due to Boyd, Iwata and Takazawa (2013), who designed a 6/5-approximation algorithm for 3-edge connected cubic graphs. Our algorithm employs the ideas in this algorithm and makes use of bipartiteness to attain a better ratio 7/6.