multiwaymergesort

Multiwaymergesort is a generalization of the classic mergesort that sorts by repeatedly dividing the input into k sublists, sorting each sublist, and then merging the k sorted sublists back into a single sorted sequence. The parameter k, known as the branching factor, can be tuned; k = 2 yields the standard binary mergesort, while larger k reduces the number of recursion levels but increases the cost of the final k-way merge.

Algorithmically, multiwaymergesort splits n elements into k roughly equal parts, recursively sorts each part using the same algorithm, and then performs a k-way merge to produce the final sorted list. The k-way merge is typically implemented with a min-heap of size k, allowing the smallest head element from the k lists to be extracted repeatedly. This gives a merge time of O(n log k). The overall recurrence is T(n) = k T(n/k) + O(n log k). For fixed k, this resolves to O(n log n) time, with a constant factor that depends on k and the heap implementation.

Space usage for a straightforward implementation is usually linear in n for temporary storage, plus O(k) space for the merge heap and the recursion stack. In-place variants exist but are more complex and less common.

Applications and variants include external sorting, where large data sets exceed memory and multiway passes reduce I/O by merging multiple sorted runs; parallel or distributed implementations can sort sublists on separate processors; alternative merge strategies, such as tournament trees, may be used to optimize the merge step.