Twists Turns Cascades Deque Conjecture And Scanning Theorem
Twists Turns Cascades Deque Conjecture And Scanning Theorem
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■ Simplification 4 The sequence comprises only right cascades and left path rotations. Fur- ther, the lemma is true if the total cost of any m cascades in the sequence is 0{{m-\-n)a{m-\- n)).
Transformation. We simulate the sequence of operations on a new tree, maintaining the invariant that the original tree is a subtree of the new tree. A PARTIALPOP involving a subpath xq — xi — ■ ■ ■ — X2k is simulated by first performing a right ^'-cascade spanning the subpath Xi — X2 — • • ■ — X2k in the n...ew tree and then moving Xq up the tree using right rotations until it joins the right path. Since the cascade performs exactly half as many rotations as the PARTIALPOP, only a constant fraction of the PARTIALPOP rotations are ignored. A right rotation is simulated by rotating the corresponding edge in the new tree. ■ Lemma 10 follows from simplification 4 and Lemma 9. I The bound for the deque conjecture is derived by the following theorem: Theorem 7 The cost of performing an intermixed sequence of m deque operations on an arbitrary n-node binary tree using splaying is 0{{m + n)Q{m + n)).
What to read after Twists Turns Cascades Deque Conjecture And Scanning Theorem?
You can find similar books in the "Read Also" column, or choose other free books by R Rajamani Sundar to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
■ Simplification 4 The sequence comprises only right cascades and left path rotations. Fur- ther, the lemma is true if the total cost of any m cascades in the sequence is 0{{m-\-n)a{m-\- n)).
Transformation. We simulate the sequence of operations on a new tree, maintaining the invariant that the original tree is a subtree of the new tree. A PARTIALPOP involving a subpath xq — xi — ■ ■ ■ — X2k is simulated by first performing a right ^'-cascade spanning the subpath Xi — X2 — • • ■ — X2k in the n...ew tree and then moving Xq up the tree using right rotations until it joins the right path. Since the cascade performs exactly half as many rotations as the PARTIALPOP, only a constant fraction of the PARTIALPOP rotations are ignored. A right rotation is simulated by rotating the corresponding edge in the new tree. ■ Lemma 10 follows from simplification 4 and Lemma 9. I The bound for the deque conjecture is derived by the following theorem: Theorem 7 The cost of performing an intermixed sequence of m deque operations on an arbitrary n-node binary tree using splaying is 0{{m + n)Q{m + n)).
What to read after Twists Turns Cascades Deque Conjecture And Scanning Theorem?
You can find similar books in the "Read Also" column, or choose other free books by R Rajamani Sundar to read onlineMoreLess
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