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Concept
External sorting
Summary
External sorting is a class of sorting algorithms that can handle massive amounts of data. External sorting is required when the data being sorted do not fit into the main memory of a computing device (usually RAM) and instead they must reside in the slower external memory, usually a disk drive. Thus, external sorting algorithms are external memory algorithms and thus applicable in the external memory model of computation.
External sorting algorithms generally fall into two types, distribution sorting, which resembles quicksort, and external merge sort, which resembles merge sort. External merge sort typically uses a hybrid sort-merge strategy. In the sorting phase, chunks of data small enough to fit in main memory are read, sorted, and written out to a temporary file. In the merge phase, the sorted subfiles are combined into a single larger file.
External memory model
External sorting algorithms can be analyzed in the external memory model. In this model, a cache or internal memory of size M and an unbounded external memory are divided into blocks of size B, and the running time of an algorithm is determined by the number of memory transfers between internal and external memory. Like their cache-oblivious counterparts, asymptotically optimal external sorting algorithms achieve a running time (in Big O notation) of .
One example of external sorting is the external merge sort algorithm, which is a K-way merge algorithm. It sorts chunks that each fit in RAM, then merges the sorted chunks together.
The algorithm first sorts M items at a time and puts the sorted lists back into external memory. It then recursively does a -way merge on those sorted lists. To do this merge, B elements from each sorted list are loaded into internal memory, and the minimum is repeatedly outputted.
For example, for sorting 900 megabytes of data using only 100 megabytes of RAM:
Read 100 MB of the data in main memory and sort by some conventional method, like quicksort.
Write the sorted data to disk.
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