Minimum spanning tree of line segments

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Conference Article

Publication Title

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)


In this article, we study a variant of the geometric minimum spanning tree (MST) problem. Given a set S of n disjoint line segments in, we need to find a tree spanning one endpoint from each of the segments in S. Note that, we have 2n possible choices of such a set of endpoints, each being referred as an instance. Thus, our objective is to choose one among those instances such that the sum of the lengths of all the edges of the tree spanning the points of that instance is minimum. We show that finding such a spanning tree is NP-complete in general, and propose a (Formula Presented) -factor approximation algorithm for the same.

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