In this paper, the authors discuss the Euclidean bottleneck biconnected edge subgraph problem. They shall first define a k-relative neighborhood graph which is similar to the relative neighborhood graph first proposed by Toussaint. In a k-relative neighborhood graph, a lune contains less than k points. The authors then show that there exists a solution of the Euclidean bottleneck biconnected edge subgraph problem which is a subgraph of the 2-relative neighborhood graph. With this information, they propose an algorithm to find a Euclidean bottleneck biconnected edge subgraph as follows: (1)Construct a 2-relative neighborhood graph. (2)Use the binary search technique on the sorted edge sequence of the 2-relative neighborhood graph to find a Euclidean bottleneck biconnected edge subgraph. The construction of the 2-relative neighborhood graph takes O(n2).
