Abstract
In this paper, we discuss the Euclidean bottleneck biconnected edge subgraph problem. We 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. We then show that there exists a solution of the Euclidean bottleneck biconnected edge subgraph problem which is a subgraph of the 2-relative neigborhood graph. With this information, we 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 Eucledian bottleneck biconnected edge subgraph. The construction of the 2-relative neighborhood graph takes O( n 2)
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