Of the three, LinkedList is generally going to give you the best performance. Here’s why:
ArrayList and Vector each use an array to store the elements of the list. As a result, when an element is inserted into (or removed from) the middle of the list, the elements that follow must all be shifted accordingly. Vector is synchronized, so if a thread-safe implementation is not needed, it is recommended to use ArrayList rather than Vector.
LinkedList, on the other hand, is implemented using a doubly linked list. As a result, an inserting or removing an element only requires updating the links that immediately precede and follow the element being inserted or removed.
However, it is worth noting that if performance is that critical, it’s better to just use an array and manage it yourself, or use one of the high performance 3rd party packages such as Trove or HPPC.