Online matching on a line

Authors:
Bernhard Fuchs;Winfried Hochstättler;Walter Kern
Affiliations:
Center for Applied Computer Science Cologne, Universität zu Köln, Köln, Germany;Department of Mathematics, BTU Cottbus, Postfach, Cottbus, Germany;Department of Applied Mathematics, University of Twente, AE Enschede, Netherlands
Venue:
Theoretical Computer Science
Year:
2005

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Abstract

Given a set S ⊆ R of points on the line, we consider the task of matching a sequence (r1, r1,... ) of requests in R to points in S. It has been conjectured [Online Algorithms: The State of the Art, Lecture Notes in Computer Science, Vol. 1442, Springer, Berlin, 1998, pp. 268-280] that there exists a 9-competitive online algorithm for this problem, similar to the so-called "cow path" problem [Inform. and Comput. 106 (1993) 234-252]. We disprove this conjecture and show that no online algorithm can achieve a competitive ratio strictly less than 9.001.Our argument is based on a new proof for the optimality of the competitive ratio 9 for the "cow path" problem.