Shortest Tour of a Sequence of Disjoint Segments in L 1 Esther Arkin Applied Math and Statistics, Stony Brook University, USA Moshe Dror Management and Information Sciences, the University of Arizona Alon Efrat Computer Science, the University of Arizona Cesim Erten Computer Science and Engineering, Isik University Ferran Hurtado Matem´ atica Aplicada II, Universitat Polit´ ecnica de Catalunya Joseph S. B. Mitchell Applied Math and Statistics, Stony Brook University, USA Valentin Polishchuk Helsinki Institute for Information Technology, University of Helsinki, Finland Corresponding author. Tel: +1(775)587-2717. Fax: +1(631)632-8490. Preprint submitted to Elsevier 6 August 2007