A. L. Buchsbaum, R. Sundar, and R. E. Tarjan. Data structural bootstrapping, linear path compression, and catenable heap ordered double ended queues. In Proc. 33rd IEEE Symp. on Foundations of Computer Science, pages 40--49, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of finding the minimum element in a deque (but not deleting it) while preserv ing a constant amortized time bound for every operation, including finding the minimum. We merely have to store with each buffer, each deque, and each pair or triple the minimum element in it. For related work see [1, 2, 6, 10]. We can also support a flip operation on deques. A flip operation reverses the linear order of the elements in the deque: the ith from the front becomes the ith from the back, and vice versa. For the noncatenable deques of Section 3, we implement flip by maintaining a reversal bit that is ....

A. L. Buchsbaum, R. Sundar, and R. E. Tarjan. Data structural bootstrapping, linear path compression, and catenable heap ordered double ended queues. SIAM J. Computing, 24(6):1190-1206, 1995.

....19 5. 2 Recursive Slowdown deques Kaplan and Tarjan describe in [KT95] a technique for structuring data type representations which they call recursive slowdown, adapting ideas from the so called segmented binary numbers implementation (see for example Chapter 3 of [Oka96b] and from the work on [BST92]. They use this technique to implement deques and catenable deques with constant time operations even with persistent use. Their data structure is described for an imperative language (using pointers) but in an applicative style and taking care to maintain persistence, which requires some copying ....

A. L. Buchsbaum, R. Sundar, and R. E. Tarjan. Data structural bootstrapping, linear path compression, and catenable heap ordered double ended queues. In Proceedings of the 33rd IEEE Symposium on Foundations of Computer Science, pages 40--49, 1992.

....elimination method is O(jEj Theta log(jN j) Proof: The number e of path compressions is bounded by jEj. Buchsbaum et al. have recently established the lower bound Theta(e Thetalog(n) for a sequence of e (order preserving) path compressions satisfying the RRC on an initial tree of n nodes [BST95] For most flowgraphs, jEj = O(jN j) so the above bound is tight. 6.3 Discussion Before closing this section, we want to point out some interesting features of our delayed elimination method. ffl Our D1 rule is similar to Hecht Ullman s T1 rule and Graham Wegman s T1 0 rule. Our D2a rule is ....

Buchsbaum, A. L., Sundar, R., and Tarjan, R. E. Data structural bootstrapping, linear path compression, and catenable heap ordered double ended queues (to appear). SIAM Journal of Computing, 42(5), October 1995.

....operation of finding the minimum element in a deque (but not deleting it) Each operation remains constant time, and the implementation remains purely functional. We merely have to store with each buffer, each deque, and each pair the minimum element contained in it. For related work see [3, 4, 19, 31]. We can also support a flip operation on deques, for each of the structures in Sections 4 and 6. A flip operation reverses the linear order of the elements in the deque; the ith from the front becomes the ith from the back and vice versa. For the noncatenable deques of Section 4, we implement ....

A. L. Buchsbaum, R. Sundar, and R. E. Tarjan. Data structural bootstrapping, linear path compression, and catenable heap ordered double ended queues. SIAM J. Computing, 24(6):1190--1206, 1995.

....operation of nding the minimum element in a deque (but not deleting it) while preserving a constant amortized time bound for every operation, including nding the minimum. We merely have to store with each bu er, each deque, and each pair or triple the minimum element in it. For related work see [1, 2, 6, 13]. We can also support a ip operation on deques. A ip operation reverses the linear order of the elements in the deque: the ith from the front becomes the ith from the back, and vice versa. For the noncatenable deques of Section 3, we implement ip by maintaining a reversal bit that is ipped by ....

A. L. Buchsbaum, R. Sundar, and R. E. Tarjan, Data structural bootstrapping, linear path compression, and catenable heap ordered double ended queues, SIAM J. Computing, 24 (1995), pp. 1190-1206.

....order preserving path compression. We summarize in Section 2.5. We remark that the methods used in Chapter 3, as stated there, provide a nontrivial worst case time bound per heapordered deque operation. A preliminary version of the material in this chapter appears as Buchsbaum, Sundar, and Tarjan [BST92] 2.2 Reviewing Heap Ordered Queues and Deques For completeness, we begin by reviewing how to implement heap ordered queues and heap ordered deques. As in Chapter 1, identify the head of a list (where the first element sits) as the left end of the list and the tail as the right. A minimum ....

A. L. Buchsbaum, R. Sundar, and R. E. Tarjan. Data structural bootstrapping, linear path compression, and catenable heap ordered double ended queues. In Proc. 33rd IEEE Symp. on Foundations of Computer Science, pages 40--9, 1992.

....Gabow and Tarjan [11] used a priori knowledge of the unordered set of unions to implement the union and find operations in O(m n) time. We do not require advance knowledge of the unions themselves, only that their order be constrained. Other results on improved bounds for path compression [5, 14,16] generally restrict the order in which finds, not unions, are performed. Of the n vertices, designate l to be special and the remainder n Gamma l to be ordinary. The following theorem shows that by requiring the unions to favor a small set of vertices, the time bound becomes linear. Theorem ....

A. L. Buchsbaum, R. Sundar, and R. E. Tarjan. Data-structural bootstrapping, linear path compression, and catenable heap-ordered double-ended queues. SIAM Journal on Computing, 24(6):1190--1206, 1995.

....of finding the minimum element in a deque (but not deleting it) while preserving a constant amortized time bound for every operation, including finding the minimum. We merely have to store with each buffer, each deque, and each pair or triple the minimum element in it. For related work see [1, 2, 6, 10]. We can also support a flip operation on deques. A flip operation reverses the linear order of the elements in the deque: the ith from the front becomes the ith from the back, and vice versa. For the noncatenable deques of Section 3, we implement flip by maintaining a reversal bit that is ....

A. L. Buchsbaum, R. Sundar, and R. E. Tarjan. Data structural bootstrapping, linear path compression, and catenable heap ordered double ended queues. SIAM J. Computing, 24(6):1190--1206, 1995.

....n) elements and applying this decomposition recursively. The first type of bootstrapping, which we call structural abstraction, is used by Driscoll, Sleator, and Tarjan [19] to implement persistent catenable lists using fully persistent (non catenable) lists and by Buchsbaum, Sundar, and Tarjan [6] to implement catenable heap ordered deques using non catenable heap ordered deques. It is similar to a technique used by Kosaraju [24] to design catenable deques by dissecting them and storing contiguous pieces on stacks. The second type of bootstrapping, which we call structural decomposition, ....

....to implement confluently persistent deque trees (and thus deques) The efficiency of the implementation derives from the deque tree balance property. We define a pull operation on deque trees just as Driscoll, Sleator, and Tarjan [19] define this operation on similar trees; Buchsbaum and Tarjan [6] define a slightly different form of pull. Let x be the leftmost non leaf child of the root r of a tree T , and let x 0 be the leftmost child of x. A pull on T cuts the link from x 0 to x and makes x 0 a new child of r just to the left of x. Additionally, if x is now unary, it is replaced by its ....

[Article contains additional citation context not shown here]

A. L. Buchsbaum, R. Sundar, and R. E. Tarjan. Data structural bootstrapping, linear path compression, and catenable heap ordered double ended queues. In Proc. 33rd IEEE Symp. on Foundations of Computer Science, pages 40--9, 1992.

....order preserving path compression. We summarize in Section 2.5. We remark that the methods used in Chapter 3, as stated there, provide a nontrivial worst case time bound per heapordered deque operation. A preliminary version of the material in this chapter appears as Buchsbaum, Sundar, and Tarjan [BST92] 2.2 Reviewing Heap Ordered Queues and Deques For completeness, we begin by reviewing how to implement heap ordered queues and heap ordered deques. As in Chapter 1, identify the head of a list (where the first element sits) as the left end of the list and the tail as the right. A minimum ....

A. L. Buchsbaum, R. Sundar, and R. E. Tarjan. Data structural bootstrapping, linear path compression, and catenable heap ordered double ended queues. In Proc. 33rd IEEE Symp. on Foundations of Computer Science, pages 40--9, 1992.

....Previously, Gabow and Tarjan [14] used a priori knowledge of the unordered set of unions to implement the union and find operations in O(m n) time. We do not require advance knowledge of the unions, only that their order be constrained. Other results on improved bounds for path compression [6, 21, 23] generally restrict the order in which finds, not unions, are performed. The following theorem shows that requiring the unions to favor a small set of vertices results in a linear time bound. Designate l vertices to be special and the remaining n Gamma l to be ordinary. Theorem 3.1 Consider n ....

A. L. Buchsbaum, R. Sundar, and R. E. Tarjan. Datastructural bootstrapping, linear path compression, and catenable heap-ordered double-ended queues. SIAM J. Comp., 24(6):1190--1206, 1995.

No context found.

A. L. Buchsbaum, R. Sundar and R. E. Tarjan. Data structural bootstrapping, linear path compression, and catenable heap ordered double ended queues, Proceedings of the 33rd IEEE Symp. on Foundations of Computer Science, 1992, 40--49.

No context found.

A. L. Buchsbaum, R. Sundar, and R. E. Tarjan. Data structural bootstrapping, linear path compression, and catenable heap ordered double ended queues. In Proc. 33rd IEEE Symp. on Foundations of Computer Science, pages 40--49, 1992.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC