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Abstract.A Steiner Minimal Tree (SMT) for a given set A = {a 1 ..... a,} in the plane is a tree which interconnects these points and whose total length, i.e., the sum of lengths of the branches, is minimum. To achieve the minimum, the tree may contain other points (Steiner points) besides al, ..., a,. Various improvements are presented to an earlier computer program of the authors for plane SMq~s. These changes have radically reduced machine times. The existing program was limited in application to about n = 30, while the innovations have facilitated solution of many randomly generated 100-point problems in reasonable processing times.

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In [l] Clark has obtained an asymptotic formula involving the eigenvalues of the Laplacian operator-A (with zero boundary conditions) on a "quasi-bounded" region ft in Rn. A region is called quasibounded if it cannot contain an infinite family of nonintersecting open solid w-spheres of equal size. The formula (valid under certain additional assumptions) is as follows.

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