Online algorithms for finger searching

The technique of speeding up access into search structures by maintaining fingers that point to various locations of the search structure is considered. The problem of choosing, in a large search structure, locations at which to maintain fingers is treated. In particular, a server problem in which k servers move along a line segment of length m, where m is the number of keys in the search structure, is addressed. Since fingers may be arbitrarily copied, a server is allowed to jump, or fork, to a location currently occupied by another server. Online algorithms are presented and their competitiveness analyzed. It is shown that the case in which k = 2 behaves differently from the case in which k ≥ 3, by showing that there is a four-competitive algorithm for k = 2 that never forks its fingers. For k ≥ 3, it is shown that any online algorithm that does not fork its fingers can be at most Ω(m^1/2)-competitive. The main result is that for k = 3 there is an online algorithm that forks and is constant competitive (independent of m, the size of the search structure). The algorithm is simple and implementable.