1. A computer-implemented method for adaptively and incrementally checkpointing an operator state in a data stream processing application comprising: during operation of the stream processing application, logging changes made to operator state, and one of: apply checkpointing to the operator state data according to a base checkpoint data form which saves data of a whole full operator state; or apply incremental checkpointing of only the logged changes to operator state as a delta checkpoint data in a data storage device; maintaining information about a dependency between checkpoints along with the checkpointed data; storing said dependency information in the data storage device; and upon performing a base checkpoint, determining adaptively how many subsequent checkpoints will be stored as delta checkpoints between two consecutive base checkpoints.