Author : Paul Spirakis
Publisher :
ISBN 13 : 9781332172443
Total Pages : 44 pages
Book Rating : 4.1/5 (724 download)
Book Synopsis On the Combinatorial Complexity of Motion Coordination (Classic Reprint) by : Paul Spirakis
Download or read book On the Combinatorial Complexity of Motion Coordination (Classic Reprint) written by Paul Spirakis and published by . This book was released on 2015-08-04 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from On the Combinatorial Complexity of Motion Coordination We investigate the complexity of the problem of coordinating the motion of many planar rigid objects in a two dimensional space. Each object has a simple geometrical description (it is a box or a circle). The number of objects to be moved is part of the problem size. The plane where objects move is partitioned into two regions: The region of forbidden points, being a finite union of areas each bounded by a polygonal line, and its complement. During motion, objects are not allowed to overlap or to intersect the region of forbidden points, but they are allowed to be in contact with the boundary of obstacles or other objects. We analyze several variants of the above problem of motion planning and prove that they are NP-hard, in the strong sense. We also consider simple combinatorial planar graph-and-pebble models which capture certain non-geometric aspects of coordinated motion. We provide an algorithm for planning the motion of k.pebbles in an n-vertex planar graph, which is 0(n ). We also show that coordination of motion of n-1 distinct pebbles in an n-vertex graph, from a set of n-I distinct initial to n-1 distinct final positions, can be decided and planned in polynomial time inn. Finally, we show that certain problems of planning the motion of many pebbles, when the motion is nonsymmetric, or when the final positions are required to satisfy a combinatorial property, are NP-hard in the strong sense. 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."
