In this paper we present a method to obtain optimal h-v drawings in parallel. Based on parallel tree contraction, our method computes optimal (with respect to a class of cost functions of the enclosing rectangle) drawings in O(log2 n) parallel time by using a polynomial number of EREW processors. The number of processors reduces substantially when we study minimum area drawings. Our work places the problem of obtaining optimal size h-v drawings in NC, presenting the first algorithm with polylogarithmic time complexity.
A Note on Parallel Algorithms for h-v Drawing of Binary Trees, with G.E. Pantziou and A. Symvonis. In Computational Geometry: Theory and Applications, 9 145-158 (1998).