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On Arrangements of Jordan Arcs With Three Intersections Per Pair
Excerpt from On Arrangements of Jordan Arcs With Three Intersections Per Pair
We believe that the construction Of the surface R sheds some light on how the complexity Of the exterior boundary Of the union Of a number Of Jordan regions arises out Of two [different the davenport-schinzel controlled behavior along the boundary Of this surface and then the internal fragmentation introduced by the overlap Of different flaps when projected down onto the plane. We hope that this surface construction will also be found of use in algorithmic questions, since it provides a simply connected manifold of nearly linear boundary complexity (as long as the number Of intersections per pair Of arcs is bounded) that covers an area Of the plane that can have quadratic complexity when explicitly represented.
We believe that the construction Of the surface R sheds some light on how the complexity Of the exterior boundary Of the union Of a number Of Jordan regions arises out Of two [different the davenport-schinzel controlled behavior along the boundary Of this surface and then the internal fragmentation introduced by the overlap Of different flaps when projected down onto the plane. We hope that this surface construction will also be found of use in algorithmic questions, since it provides a simply connected manifold of nearly linear boundary complexity (as long as the number Of intersections per pair Of arcs is bounded) that covers an area Of the plane that can have quadratic complexity when explicitly represented.
25 pages, Paperback
Published August 24, 2018
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