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The DSW algorithm, or in full Day/Stout/Warren algorithm, is a method for efficiently balancing binary search trees — that is, decreasing their height to O(log n) nodes, where n is the total number of nodes. Unlike a self-balancing binary search tree, it does not do this incrementally during each operation, but periodically, so that its cost can be amortized over many operations. The algorithm was designed by Quentin Stout and Bette Warren in their 1986 paper Tree Rebalancing in Optimal Time and Space, based on work done by Colin Day in 1976.

The algorithm requires linear (O(n)) time and is in-place. Besides being simpler than many earlier tree-balancing algorithms, simple enough to teach in elementary data structure classes, it can also be easily modified to balance trees perfectly; that is, such that no two leaves differ in depth by more than one. This is a useful transformation to perform if it is known that no more inserts will be done.

A 2002 article by Timothy J. Rolfe has recently brought attention back to the DSW algorithm after a long hiatus; there is evidence that it is he who first named it the DSW algorithm. He cites two main advantages: "in circumstances in which one generates an entire binary search tree at the beginning of processing, followed by item look-up access for the rest of processing" and "pedagogically within a course on data structures where one progresses from the binary search tree into self-adjusting trees, since it gives a first exposure to doing rotations within a binary search tree."

• An explanation and some experiments by Timothy J. Rolfe
• The original paper by Stout and Warren

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