Online matching on a line

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Abstract

Given a set SR of points on the line, we consider the task of matching a sequence (r1,r2,) 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.

Keywords

Competitive analysis
Matching
Online algorithms

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Supported by Deutsche Forschungsgemeinschaft, Graduiertenkolleg Scientific Computing, GRK 192/5-02.