TEL-AVIV UNIVERSITY RAYMOND AND BEVERLY SACKLER FACULTY OF EXACT SCIENCES SCHOOL OF COMPUTER SCIENCE Efficient Construction of Pathways in the Complement of the Union of Balls in R 3 Thesis submitted in partial fulfillment of the requirements for the M.Sc. degree in the School of Computer Science, Tel-Aviv University by Eitan Yaffe The research work for this thesis has been carried out at Tel-Aviv University under the supervision of Prof. Dan Halperin September 2007