On stars and Steiner stars

A Steiner star for a set P of n points in Rd connects an arbitrary point in Rd to all points of P, while a star connects one of the points in P to the remaining n - 1 points of P. All connections are realized by straight line segments. Let the length of a graph be the total Euclidean length of its edges. Fekete and Meijer showed that the minimum star is at most 2 times longer than the minimum Steiner star for any finite point configuration in Rd . The supremum of the ratio between the two lengths, over all finite point configurations in Rd , is called the star Steiner ratio in Rd . It is conjectured that this ratio

• Type: Conference
• Year: 2008
• Where: SODA
• Authors: Adrian Dumitrescu, Csaba D. Tóth
• Keywords: Algorithms, Finite Point Configurations, SODA 2008, Steiner Star, Total Euclidean Length