Showing papers by "Center for Discrete Mathematics and Theoretical Computer Science published in 1992"
TL;DR: In this article, Gilbert and Pollak gave a proof for their conjecture and showed that for any point on the euclidean plane, the length of the Steiner minimum tree and the minimum spanning tree can be computed in polynomial time.
Abstract: LetP be a set ofn points on the euclidean plane. LetL
s(P) andL
m
(P) denote the lengths of the Steiner minimum tree and the minimum spanning tree onP, respectively. In 1968, Gilbert and Pollak conjectured that for anyP,L
s
(P)≥(√3/2)L
m
(P). We provide a proof for their conjecture in this paper.
146 citations
61 citations