General splay: A basic theory and calculus

Abstract

For storage and retrieval applications where access frequencies are biased, uniformly-balanced search trees may be suboptimal. Splay trees address this issue, providing a means for searching which is statically optimum and conjectured to be dynamically optimum. Subramanian explored the reasons for their success, expressing local transformations as templates and giving sufficient criteria for a template family to exhibit amortized O(logN) performance. We present a different formulation of the potential function, based on progress factors along edges. Its decomposition w.r.t. a template enables us to relax all of Subramanian's conditions. Moreover it illustrates the reasons why template-based self-adjustment schemes work, and provides a straightforward way of evaluating the efficiency of such schemes.