Connect points with polylines + polylines does not intersect

Hi I've got a problem I would like to solve.
Is there a way to programatically connect points with polylines(it's simple) under such conditions:

-polylines doesn't intersect with each other(example_1.png and example_2.png in attachments)
-each pair of points can only have one polyline beetwen them, routes cannot be shared(look at attachments 3rd .png file)
-if there is no way that polylines doesn't intersect I want to minimize the number of intersections

I don't need the whole code for this I just need few tips:)
Thanks.

Regards,
MDruzgala

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