Rehabilitation of an unloved child: semi-splaying

Splay trees are widely considered as the classic examples of self-adjusting binary search trees and are part of probably every course on data structures and algorithms. Already in the first seminal paper on splay trees [7] alternative operations were introduced, among which semi-splaying. On the one hand the analysis of semi-splaying gives a smaller constant for the amortized complexity, however on the other hand the authors write: Whether any version of semi-splaying is an improvement over splaying depends on the access sequence. Semi-splaying may be better when the access pattern is stable, but splaying adapts much faster to changes in usage. Maybe this sentence was the reason that nobody seriously ran tests to compare the performance of semi-splaying and splaying. Semi-splaying is conceptually simpler than splaying, has the same asymptotic amortized complexity and, as will be clear from empirical data presented in this paper, the practical performance is better for almost all kinds of access sequences. So due to its efficiency there are good reasons to use semi-splaying instead of its more prominent brother for applications. Moreover, its simplicity makes it also very attractive for teaching. Copyright c © 2006 John Wiley & Sons, Ltd.