Long non-crossing configurations in the plane (Draft)
نویسندگان
چکیده
It is shown that for any set of 2n points in general position in the plane there is a non-crossing perfect matching of n straight line segments whose total length is at least 2/π of the maximum possible total length of a (possibly crossing) perfect matching on these points. The constant 2/π is best possible and a non-crossing matching whose length is at least as above can be found in polynomial time. Similar results are obtained for the problem of finding a long non-crossing Hamilton path and a long non-crossing spanning tree for a given set of points in the plane.
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تاریخ انتشار 2002