Polynomial Area Bounds for MST Embeddings of Trees

In their seminal paper on geometric minimum spanning trees, Monma and Suri [11] showed how to embed any tree of maximum degree 5 as a minimum spanning tree in the Euclidean plane. The embeddings provided by their algorithm require area O(2n2) × O(2n2) and the authors conjectured that an improvement below cn×cn is not possible, for some constant c > 0. In this paper, we show how to construct MST embeddings of arbitrary trees of maximum degree 3 and 4 within polynomial area.