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Excerpt from Separating Two Simple Polygons, by a Sequence of Translations Let P and Q be two disjoint simple polygons having m and n sides respectively. We present an algorithm which determines whether Q can be moved by a sequence of translations to a position sufficiently far from P without colliding with P, and which produces such a motion if it exists. Our algorithm runs in time O(mn a(mn) log m log n) where a(k) is the extremely slowly growing inverse Ackermann's function. Since. In the worst ease O(mn) translations may be necessary to separate Q from P, our algorithm is close to optimal. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com 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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