Sum of Squared Edges for MST of a Point Set in a Unit Square

O. Aichholzer, S. Allen, G. Aloupis, L. Barba, P. Bose, J.-L. D. Carufel, J. Iacono, S. Langerman, D. Souvaine, P. Taslakin, and M. Yagnatinsky

Abstract:

Given a set P of points in the unit square let w(P) be the minimum sum of the squares of the edge lengths in the minimum spanning tree of P. We show that w(P) < 3.411.

Reference: O. Aichholzer, S. Allen, G. Aloupis, L. Barba, P. Bose, J.-L. D. Carufel, J. Iacono, S. Langerman, D. Souvaine, P. Taslakin, and M. Yagnatinsky. Sum of squared edges for mst of a point set in a unit square. In Proc. of the $16^{th}$ Japan Conference on Discrete and Computational Geometry and Graphs (JCDCG$^2$ 2013), Tokyo, Japan, 2013.