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 effects: 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 ...
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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 effects: 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. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at ... This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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