Robust and Adaptive Search

Binary search finds a given element in a sorted array with an optimal number of log n queries. However, binary search fails even when the array is only slightly disordered or access to its elements is subject to errors. We study the worst-case query complexity of search algorithms that are robust to imprecise queries and that adapt to perturbations of the order of the elements. We give (almost) tight results for various parameters that quantify query errors and that measure array disorder. In particular, we exhibit settings where query complexities of log n + ck, (1+epsilon) log n + ck, and sqrt(cnk)+o(nk) are best-possible for parameter value k, any epsilon > 0, and constant c

Adaptive search over sorted sets

We revisit the classical algorithms for searching over sorted sets to introduce an algorithm refinement, called Adaptive search, that combines the good features of Interpolation search and those of Binary search. W.r.t. Interpolation search, only a constant number of extra comparisons is introduced. Yet, under diverse input data distributions our algorithm shows costs comparable to that of Interpolation search, i.e., O(log logn) while the worst-case cost is always in O(logn), as with Binary search. On benchmarks drawn from large datasets, both synthetic and real-life, Adaptive search scores better times and lesser memory accesses even than Santoro and Sidney’s Interpolation–Binary search