On the Competitiveness of Linear Search

We re-examine offline techniques for linear search. Under a reasonable model of computation, a method is given to perform offline linear search in amortized cost proportional to the entropy of the request sequence; and so, this cost is at most logarithmic. On the other hand, any online technique is subject to linear amortized cost for some sequences. It follows, then, that no online technique can have an amortized cost of that which one could obtain if given the request sequence in advance, i.e., there is no competitive linear search algorithm.