Binary Searching with Non - uniform

We study the problem of minimizing the expected cost of binary searching for data where the access cost is not xed and depends on the last accessed element, such as data stored in magnetic or optical disk. We present an optimal algorithm for this problem that nds the optimal search strategy in O(n 3) time, which is the same time complexity of the simpler classical problem of xed costs. Next, we present two practical linear expected time algorithms, under the assumption that the access cost of an element is independent of its physical position. Both practical algorithms are online, that is, they nd the next element to access as the search proceeds. The rst one is an approximate algorithm which minimizes the access cost disregarding the goodness of the problem partitioning. The second one is a heuristic algorithm, whose quality depends on its ability to estimate the nal search cost, and therefore it can be tuned by recording statistics of previous runs. We present an application for our algorithms related to text retrieval. When a text collection is large it demands specialized indexing techniques for eecient access. One important type of index is the suux array, where data access is provided through an indirect binary search on the text stored in magnetic disk or optical disk. Under this cost model we prove that the optimal algorithm cannot perform better than (1= log n) times the standard binary search. We also prove that the approximate strategy cannot, on average, perform worse than 39% over the optimal one. We connrm the analytical results with simulations, showing improvements between 34% (optimal) and 60% (online) over standard binary search for both magnetic and optical disks.