Simulation of Wet Film Evolution and the Euclidean Steiner Problem
Volume 10, Issue 4 (1999), pp. 457–466
Pub. online: 1 January 1999
Type: Research Article
Received
1 November 1999
1 November 1999
Published
1 January 1999
1 January 1999
Abstract
The Steiner problem asks for the shortest network that spans a given set of fixed points in the Euclidean plane. The problem is NP hard.
The result of simulation of an idealized “wet” film connecting fixed points is a length-minimizing curve. Increasing the exterior pressure step by step we are able to achieve the film configuration near to the Steiner minimal tree. “Dead-point” situations may occur for some symmetric allocation of fixed points.
The limited simulation experiments show that the average computation time depends almost linearly on the number of fixed points for the situations without “dead-points”.