Polynomial area bounds for MST embeddings of trees

In their seminal paper on geometric minimum spanning trees, Monma and Suri (1992) [31] 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(n22)×O(n22)O(2n2)×O(2n2) and the authors conjectured that an improvement below cn×cncn×cn is not possible, for some constant c>0c>0. In this paper, we show how to construct MST embeddings of arbitrary trees of maximum degree 3 and 4 within polynomial area.