In 1990's, the paper Unifying Maximum Cut and Minimum Cut of a Planar Graph described an$O(n^{3/2}\log n)$-time algorithm for Weighted Planar Max Cut, a landmark in the field. Recently, this paper appeared:Min st-Cut Oracle for Planar Graphs with Near-Linear Preprocessing Time   http://arxiv.org/abs/1003.1320I was wondering if the time for Weighted Planar Max Cut could be improved from $O(n^{3/2}\log n)$ to $O(n \log^c n)$ for some small constant $c$, using ideas from this paper?In general, have any improvements in Weighted Planar Max Cut been published?
What is the fastest algorithm for Weighted Planar Max Cut
time complexity