A binary type of this operation can produce an output in Big O of log n time on a sorted list by always picking the middle element of a sublist.  
Grover's Algorithm provides a mechanism for doing this operation in Big O of squareroot of n time on a quantum computer.  One way to optimize this operation is with a genetic algorithm and a well built hash table can perform this operation in constant time.  A binary type of this operation can produce an output in Big O of log n time on a sorted list by always picking the middle element of a sublist.  In graph theory, this can be done in a breadth first or depth first fashion.  For 10 points, identify this type of algorithm that, unsurprisingly, finds an element in a data structure.
Grover's Algorithm provides a mechanism for doing this operation in Big O of squareroot of n time on a quantum computer.  
{Searching} Algorithms (also accept things like {Lookup Algorithms}; prompt on "{Query}" since that's a related but different operation)