On Thu, Feb 22, 2007 at 07:19:52PM -0600, Matt Gokey wrote: > Here is a thought experiment to test: define the board only logically > using a graph (nodes and neighbor nodes). No topological shape and no > mesh layout over any shape is needed. If all nodes have exactly four > neighbors, there is no method or algorithm that you can run to find an > edge. All nodes will look equivalent.
Sure, but not all such boards are equivalent anyway! Add a stone to the board. Add another stone to one of its liberties. Add a third stone to any (empty) liberty of the last stone. There are three possibilities. Choose the one that maximises the liberties of the string. You have now defined a straight line. Continue this line until you meet a black stone (which must be part of the original line). I guess you meet the beginning of the line, where it all started. How big portion of the board is now filled with black stones? That can vary depending on the properties of the grid. In the simple case you have drawn a circle of a fairly small size (say 19). In another simple case you have filled the whole board, and used many more stones (say 361). In some cases you have filled half the available points, or some other fraction. How big will this fraction be on a totally random grid? -H -- Heikki Levanto "In Murphy We Turst" heikki (at) lsd (dot) dk _______________________________________________ computer-go mailing list computer-go@computer-go.org http://www.computer-go.org/mailman/listinfo/computer-go/
