Splay trees: a reweighing lemma and a proof of competitiveness vs. dynamic balanced trees

Chain-splay trees, or, how to achieve and prove -competitiveness by splaying

“…We would also like to draw the reader's attention to [11] where it is proved that splay trees are competitive to parametrically balanced self-adjusting trees-a class including the self-adjusting versions of almost all balanced trees designed so far. Can we extend [11] to prove that chain-splaying or, better, splaying itself, is competitive to tango-trees?…”

“…Can we extend [11] to prove that chain-splaying or, better, splaying itself, is competitive to tango-trees?…”

“…trees are dynamically optimal, in other words, competitive with respect to any off-line searching algorithm that uses a binary search tree. (The reader can trace the history of splay trees and several related issues in [2,4,[6][7][8][9][10][11][12][13][14][15]17,[19][20][21][22]25]. )…”

“…The structure obtained in [9]-although it is self-organizing-it is not splay-like in the following sense: splay and splay-like search trees maintain no explicit balancing condition. (This appears to be an obligatory condition for optimal- ity: in [11] it is shown that splay trees are competitive to any known class of search trees that maintain even a minimum balance. )…”

Embedding height balanced trees and Fibonacci trees in hypercubes

“…Subsequently, however, several variations of these trees have been studied. For these variations and several other aspects of AVL trees, see [2,4,9,21]. Definition 1.1 An AVL tree is a binary search tree that has an additional balance condition that, for any vertex in the tree, the height of the left and right subtrees can differ by at most 1.…”