On the area requirements of Euclidean minimum spanning trees

• In their seminal paper on Euclidean minimum spanning trees, Monma and Suri (1992) proved that any tree of maximum degree 5 admits a planar embedding as a Euclidean minimum spanning tree. Their algorithm constructs embeddings with exponential area; however, the authors conjectured that there exist n-vertex trees of maximum degree 5 that require c(n) x c(n) area to be embedded as Euclidean minimum spanning trees, for some constant c > 1. In this paper, we prove the first exponential lower bound on the area requirements for embedding trees as Euclidean minimum spanning trees.

Subject headings

NATURVETENSKAP  -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences -- Computer Sciences (hsv//eng)

Keyword

Euclidean minimum spanning tree

Minimum area

Lower bound

Computational geometry

Publication and Content Type

ref (subject category)

art (subject category)