Schoenmakers B. Data Structures and Amortized Complexity in a Functional Setting. Ph.D. thesis, Eindhoven University of Technology, Eindhoven, Netherlands (1992).  Home/Search   Document Details and Download   Summary   Related Articles   Check

....to some deterministic selection algorithms. 1 Introduction How to design and implement efficient aggregate data structures has been a major concern for both the designers and users of functional programming languages. See, for example, Chuang and Goldberg [2, 3] Okasaki [9] Schoenmakers [11] and Shao, Reppy, and Appel [13, 14] The problem becomes more complicated if access patterns to aggregates are highly variant, or even unpredictable. A common situation occurs where there are several representations of an aggregate, with one representation being more efficient than the others for ....

Berry Schoenmakers. Data Structures and Amortized Complexity in a Functional Setting. PhD thesis, Department of Mathematics and Computing Science, Eindhoven University of Technology, September 1992.

....of findMin and merge to O(1) worst case time using the bootstrapping transformation of Brodal and Okasaki [2] The O(log n) bound for deleteMin is unaffected by this transformation. 6 Related Work There has been very little previous work on amortized functional data structures. Schoenmakers [22] used functional notation to aid in deriving bounds for many amortized data structures, but considered only single threaded data structures. Gries [6] Burton [3] and Hoogerwoord [9] described purely functional queues and double ended queues with amortized bounds, but, again, supported only ....

Berry Schoenmakers. Data Structures and Amortized Complexity in a Functional Setting. PhD thesis, Eindhoven University of Technology, 1992.

....(Williams, 1964; Crane, 1972; Vuillemin, 1978; Fredman Tarjan, 1987; Brodal, 1996) However, all of these consider only imperative priority queues. Very little has been written about purely functional priority queues. To our knowledge, only Paulson (1991) Kaldewaij and Schoenmakers (1991) Schoenmakers (1992), and King (1994) have explicitly treated priority queues in a purely functional setting. We consider priority queues that support the following operations: findMin (q) Return the minimum element of queue q. insert (x; q) Insert the element x into queue q. meld (q 1 ; q 2 ) Merge queues q 1 and ....

....a purely functional implementation of binomial queues. Although binomial queues are considered to be rather complicated in imperative settings (Jones, 1986) King demonstrates that the more convenient list processing capabilities of functional languages support binomial queues quite elegantly. Schoenmakers (1992), extending earlier work with Kaldewaij (1991) uses functional notation to aid in the derivation of amortized bounds for a number of data structures, including three priority queues: skew heaps y (Sleator Tarjan, 1986) Fibonacci heaps (Fredman Tarjan, 1987) and pairing heaps (Fredman et ....

Schoenmakers, B. (1992) Data Structures and Amortized Complexity in a Functional Setting. PhD thesis, Eindhoven University of Technology.

....original image. The above drawback leads one to another approach, which is to design efficient algorithms to make aggregates fully persistent (i.e. purely functional) such that, after a sequence of updates, the newest version as well as all previous versions of the aggregate are still accessible [1, 5, 6, 8, 9, 10, 11, 15, 19, 22]. The challenge is to reduce as much as possible the associated overhead when maintaining multiple versions of an aggregate. In this paper, we develop a randomization technique for the efficient implementation of multiple functional arrays. The expected performance of the randomized implementation ....

....form representation, however, it still provides the same functionality. This separation of representation and functionality of an evaluated expression is a key design in the shallow binding scheme, the randomization scheme, and several other efficient implementations of functional aggregates [9, 11, 22]. It has been suggested that cuts to rerooting paths have some beneficial effects to garbage collection [14] For example, in the final configuration of Figure 3, the segment with arrays E and F can be garbage collected if the only remaining references are to arrays D and G. However, we cannot ....

Berry Schoenmakers. Data Structures and Amortized Complexity in a Functional Setting. PhD thesis, Deaprtment of Mathematics and Computing Science, Eindhoven University of Technology, September 1992.

....results are compared to those of deterministic selection strategies. 1 Introduction How to design and implement efficient aggregate data structures has been a major concern for both the designers and users of functional programming languages [1] 2] 3] 5] 6] 7] 11] 14] 17] 18] 20] [23] [25] 26] The problem becomes more complicated if access patterns to aggregates are highly variant, or even unpredictable. A common situation is where there are several representations of an aggregate, with one representation more efficient than the others for certain operations but worst for ....

Berry Schoenmakers. Data Structures and Amortized Complexity in a Functional Setting. PhD thesis, Department of Mathematics and Computing Science, Eindhoven University of Technology, September 1992.

....and Tarjan. By carefully deriving requirements on that are sucient and necessary for (2) to hold, we showed in addition that this bound is minimal for the class of sum of logs potentials. 6 Along the same lines, path reversal [2] and the two pass variant of pairing [1] can be analyzed (see [4]) In all these analyses a sum of logs potential arises. As the authors of [2] note, this is easy to explain for splaying and pairing, since there is a clear connection between these operations (see [1, p.121] But they are at a loss to explain that such a potential can also be used to amortize ....

Schoenmakers B. Data Structures and Amortized Complexity in a Functional Setting. Ph.D. thesis, Eindhoven University of Technology, Eindhoven, Netherlands (1992).

....it is worthwhile to program meld performing a single pass over the rightmost paths, while at the same time building up the leftmost path (see [9] As shown in [3] it is then possible to get a simple implementation of mergeable priority queues that permits an interesting degree of concurrency. In [4, 8] the following upper bounds have been proven for the amortized costs of the operations in terms of comparisons (each unfolding of meld:x:y requires one comparison if Appears in Information Processing Letters 61(5) 279 284, March 14, 1997 y DigiCash, Kruislaan 419, 1098 VA Amsterdam, ....

....terminates as soon as the end of the rightmost path of either x or y is reached. It is also possible to define meld such that melding continues until both rightmost paths are completely traversed. The same bounds apply to this version of meld. Actually, this version was analyzed in [4] and in [8] it was shown that the same upper bounds hold for both versions. It would be interesting to extend our results to bottom up skew heaps as well. In [8] several sets of amortized bounds have been derived. Just as for top down skew heaps, operations empty, isempty, single, and min all take O(1) ....

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B. Schoenmakers, Data Structures and Amortized Complexity in a Functional Setting, Ph.D. thesis, Eindhoven University of Technology, Eindhoven, The Netherlands (1992).

.... Phi that are sufficient and necessary for (2) to hold, we showed in addition that this bound is minimal for the class of sum of logs potentials. Information Processing Letters 45 (1993) 41 50 Along the same lines, path reversal [2] and the two pass variant of pairing [1] can be analyzed (see [4]) In all these analyses a sum of logs potential arises. As the authors of [2] note, this is easy to explain for splaying and pairing, since there is a clear connection between these operations (see [1, p.121] But they are at a loss to explain that such a potential can also be used to amortize ....

Schoenmakers B. Data Structures and Amortized Complexity in a Functional Setting. Ph.D. thesis, Eindhoven University of Technology, Eindhoven, Netherlands (1992).

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