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Feb 17, 2013 at 16:03 comment added Manfred Weis @günter: it follows from the triangle inequality, that the pair of edges that constitutes to the maximal matching corresponds to the diagonals of a convex quadrilateral. So the problem is not to determine the diagonals, but rather whether they intersect each other.
Feb 17, 2013 at 13:06 comment added Günter Rote I wonder what the phrase "plus their adjacency relations" in the problem statement should mean. If if means that we know which of the distances represent edges, and which represent diagonals, then this example does not work.
Feb 17, 2013 at 5:04 history answered Włodzimierz Holsztyński CC BY-SA 3.0