A linear time algorithm for computing hexagonal Steiner minimum trees for terminals on the boundary of a regular hexagon

In this paper, we present a linear time algorithm for computing the hexagonal Steiner minimum tree for a set of points on the boundary of a regular hexagon. Computational results on randomly generated test problems show that our algorithm can find the optimal solutions on a 200 MHz Pentium within 18 seconds for n as large as 20000. It is expected that techniques of this paper may be generalized to the case where the points are on the boundary of a polygon.