Technical Perspective: Optimal Algorithms for Multiway Search on Partial Orders

Given a list of comparable items A = {a1, . . . , an sorted so that a1 < a2 < . . . < an, a canonical problem is locating a target item q within A if it exists. The canonical algorithm for this problem, of course, is binary search, which locates q using at most O(log n) comparisons between q and elements of A. Binary search is an indispensable tool for totally ordered datasets. However, many naturally occurring datasets are only partially ordered (posets), meaning that not all pairs of elements are comparable. Every such poset can be expressed as a directed acyclic graph (DAG), with edges (x,y) representing the relation x < y.