Real-time deques, multihead Turing machines, and purely functional programming

Chuang, Tyng-Ruey; Goldberg, Benjamin

doi:10.1145/165180.165225

Cited by 22 publications

(13 citation statements)

References 25 publications

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“…In his thesis, Hood [8] extended this design to the double-ended case. Chuangand Goldberg [3] laterre-inventedHood's datastructure. Okasaki [16] simplified these implementationsof queues and deques using lazy evaluation.…”

Section: Related Workmentioning

confidence: 99%

Catenable double-ended queues

Okasaki

1997

Proceedings of the Second ACM SIGPLAN International Conference on Functional Programming

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Catenabledouble-ended queues are double-ended queues (deques) thatsupportcatenation(i.e., append)efficiently without sacrificing the efficiency of other operations. We present a purely functional implementationof catenable deques for which every operation, including catenation,takea0(1) amortizedtime. Kaplan and Tarjan haveindependentlydeveloped a much more complicated implementationof crdenabledeques thatachieves similar worst-casebounds. The two designs are superficially similar, but differ in the underlying mechanismused to achieve efficiency in a persistentsetting(i.e., whenused in a non-single-threadedfashion). Their implementation uses a techniquecalled recursiveslowdown, while ours relies on the simpler mechanism of lazy evaluation.Besides lazy evaluation, our implementation rdso exemplifies theuse of two additional language features: polymorphic recursion and views. Neitheris indispensable, but both significantly simplify the presentation.

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Section: Related Workmentioning

confidence: 99%

Catenable double-ended queues

Okasaki

1997

Proceedings of the Second ACM SIGPLAN International Conference on Functional Programming

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“…It is a consequence of the ordering -a longer SL-pair that does not have a larger sum need not be kept. This is a hint that we can implement the set of SL-pairs as a double-ended queue [8]. Newer and shorter elements are added to the front end, keeping the SL-pairs sorted by length.…”

Section: An Efficient Representation Of Sets Of Prefix Sumsmentioning

confidence: 99%

Maximum segment sum is back

2008

Proceedings of the 2008 ACM SIGPLAN Symposium on Partial Evaluation and Semantics-Based Program Manipulation

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It may be surprising that variations of the maximum segment sum (MSS) problem, a textbook example for the squiggolists, are still active topics for algorithm designers. In this paper we examine the new developments from the view of relational program calculation. It turns out that, while the classical MSS problem is solved by the Greedy Theorem, by applying the Thinning Theorem, we get a linear-time algorithm for MSS with upper bound on length. To derive a linear-time algorithm for the maximum segment density problem, on the other hand, we purpose a variation of thinning based on an extended notion of monotonicity. The concepts of left-negative and right-screw segments emerge from the search for monotonicity conditions. The efficiency of the resulting algorithms crucially relies on exploiting properties of the set of partial solutions and design efficient data structures for them.

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“…See also Gajewska and Tarjan [1986] and Sarnak [1986]. Chuang and Goldberg [1993] give a particularly nice description of the deque simulation. gives a variation of this simulation that uses "memoization" to avoid some of the explicit stack-to-stack copying; his solution gives persistence but is not purely functional since memoization is a side effect.…”

Section: Previous Workmentioning

confidence: 99%

“…See, for example,Burton [1982],Chuang and Goldberg [1993],Gajewska and Tarjan [1986],Gries [1981],Hood [1982],Hood and Melville [1981],Hoogerwood [1992],,and Sarnak [1986].…”

mentioning

confidence: 99%

Purely functional, real-time deques with catenation

Kaplan

Tarjan

1999

J. ACM

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We describe an efficient, purely functional implementation of deques with catenation. In addition to being an intriguing problem in its own right, finding a purely functional implementation of catenable deques is required to add certain sophisticated programming constructs to functional programming languages. Our solution has a worst-case running time of O(1) for each push, pop, inject, eject and catenation. The best previously known solution has an O(log* k) time bound for the kth deque operation. Our solution is not only faster but simpler. A key idea used in our result is an algorithmic technique related to the redundant digital representations used to avoid carry propagation in binary counting.

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Real-time deques, multihead Turing machines, and purely functional programming

Cited by 22 publications

References 25 publications

Catenable double-ended queues

Catenable double-ended queues

Maximum segment sum is back

Purely functional, real-time deques with catenation

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