Online matching on a line
Given a set S C R 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. (c) 2004 Elsevier B.V. All rights reserved.
matching online algorithms competitive analysis