The Tourist in the Shopping Arcade 1 Rudolf Fleischer (Fudan University, Shanghai, China rudolf@acm.org) Tom Kamphans (Braunschweig University of Technology, Germany tom@kamphans.de) Rolf Klein (University of Bonn, Germany Rolf.Klein@uni-bonn.de) Elmar Langetepe (University of Bonn, Germany Elmar.Langetepe@cs.uni-bonn.de) Gerhard Trippen (University of British Columbia, Vancouver, Canada Gerhard.Trippen@sauder.ubc.ca) Abstract: A tourist is searching for a gift and moves along a shopping arcade until the desired object gets into sight. The location of the corresponding shop is not known in advance. Therefore in this on-line setting the tourist has to make a detour in comparison to an optimal off-line straight line path to the desired object. We can show that there is a strategy for the tourist, so that the path length is never greater than C * times the optimal off-line path length, where C * =1.059401 ... holds. Furthermore, there is no strategy that attains a competitive factor smaller than C * . Key Words: Computational geometry, on-line algorithms, on-line navigation. Category: F.2, G.2 1 Introduction He, who travels, often feels the need to buy some souvenirs, to prove the greatness of the sites he saw to those who could not join him on his trip. While, generally, 1 This work was begun while the third author was visiting HKUST in March 2002. The work described in this paper was partially supported by the National Natural Science Fund China (grant no. 60573025), by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKUST6010/01E) and by a grant from the Germany/Hong Kong Joint Research Scheme sponsored by the Research Grants Council of Hong Kong and the German Academic Exchange Service (Project No. G-HK024/02). Journal of Universal Computer Science, vol. 16, no. 5 (2010), 676-685 submitted: 30/7/09, accepted: 12/2/10, appeared: 1/3/10  J.UCS