We present skip-splay, the first binary search tree algorithm known to have a running time that nearly achieves the unified bound. Skip-splay trees require only O(m lg lg n + UB(σ)) time to execute a query sequence σ = σ1 . . . σm. The skip-splay algorithm is simple and similar to the splay algorithm.

In this thesis, we introduce a new binary search tree data structure called multi-splay tree and prove that multi-splay trees have most of the useful properties different binary search trees (BSTs) have. First, we demonstrate a close variant of the splay tree access lemma [ST85] for multi-splay trees, a lemma that implies multi-splay trees have the O(log n) runtime property, the static finger p...

We demonstrate the relevance of saddle-splay elasticity in nematic liquid crystalline fluids in the context of complex surface anchoring conditions and the complex geometrical confinement. Specifically, nematic cells with patterns of surface anchoring and colloidal knots are shown as examples where saddle-splay free energy contribution can have a notable role which originates from nonhomogeneou...

Splay trees are self-adjusting binary search trees which were invented by Sleator and Tarjan [1]. This entry provides executable and verified functional splay trees. The amortized complexity of splay trees is analyzed in the AFP entry Amortized Complexity.

Identification of genetic and physiological mechanisms underlying a drug's or mutation's effects on motor performance could be aided by the existence of a simple observation-based rating scale of ataxia for mice. Rating scales were developed to assess ataxia after ethanol (2.75, 3.0, and 3.25 g/kg) in nine inbred mouse strains. Each scale independently rates a single behavior. Raters, blinded t...

Problem 1. No. Couterexample (see Figure 1). If we start with the tree on the left and perform splay(2), then there is no sequence of splay operations to return to the starting tree. Note that we have enumerated all possible splay operations from each tree in the right side of the figure, since there are only 3 possible nodes to splay and one of them is the root (hence splaying it would result ...

First order splay faults, as defined here, are secondary faults that form at acute angles symmetrically on either side of a primary fault of the same sense of shear. We show that these faults form when the primary fault becomes critically misaligned with the principal stresses such that splay fault formation, on the optimum plane for faulting, is favored. First order splay faults, in distinctio...