A quantum algorithm that performs this operation i
A quantum algorithm that performs this operation in Big O of N to the one half time is called Grover's Algorithm.  Heuristic approaches to these algorithms include the Beam type, and one of the simplest examples recursively divides the dataset into two along a median and is known as the binary type.  Examples of this type of operation on a graph include Breadth-First and Depth-First.  FTP name these types of algorithms, famous examples of which include those that power Bing and Google to help you find things.
A quantum algorithm that performs this operation in Big O of N to the one half time is called Grover's Algorithm.  
{Search} Algorithms [accept equivalents like {Lookup} Algorithms]