A Lower Bound for Two-Server Balancing Algorithms

We consider the class of balancing algorithms for two servers. Such algorithms have appeared in a number of the early papers on this problem; they are so named because they seek to ``balance'''' the distance travelled evenly among the servers. In this paper, we show a universal lower bound on the competitive ratio of any balancing algorithm for two servers. The lower bound is equal to (5 + $\sqrt{7}$)/2 ($\sim$ 3.82), and consequently shows that no optimal on-line algorithm for two servers can be expressed as a balancing algorithm.

[1]  Sandy Irani,et al.  A Competitive 2-Server Algorithm , 1991, Inf. Process. Lett..

[2]  Marek Chrobak,et al.  On Fast Algorithms for Two Servers , 1991, J. Algorithms.

[3]  Lyle A. McGeoch,et al.  Competitive Algorithms for Server Problems , 1990, J. Algorithms.

[4]  Marek Chrobak,et al.  A New Approach to the Server Problem , 1991, SIAM J. Discret. Math..

[5]  Robert E. Tarjan,et al.  Amortized efficiency of list update and paging rules , 1985, CACM.

[6]  Marek Chrobak,et al.  New results on server problems , 1991, SODA '90.