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Purely Functional, RealTime Deques with Catenation
 Journal of the ACM
, 1999
"... 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 ..."
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Cited by 14 (2 self)
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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 worstcase 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 k 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.
Simple Confluently Persistent Catenable Lists
 SIAM JOURNAL ON COMPUTING
, 1998
"... We consider the problem of maintaining persistent lists subject to concatenation and to insertions and deletions at both ends. Updates to a persistent data structure are nondestructive  each operation produces a new list incorporating the change, while keeping intact the list or lists to which it a ..."
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Cited by 12 (2 self)
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We consider the problem of maintaining persistent lists subject to concatenation and to insertions and deletions at both ends. Updates to a persistent data structure are nondestructive  each operation produces a new list incorporating the change, while keeping intact the list or lists to which it applies. Although general techniques exist for making data structures persistent, these techniques fail for structures that are subject to operations, such as catenation, that combine two or more versions. In this paper we develop a simple implementation of persistent doubleended queues with catenation that supports all deque operations in constant amortized time. Our implementation is functional if we allow memoization.
Optimal Solutions for the Temporal Precedence Problem
"... In this paper we refer to the Temporal Precedence Problem on Pure Pointer Machines. This problem asks for the design of a data structure, maintaining a set of stored elements and supporting the following two operations: insert and precedes. The operation insert(a) introduces a new element a in th ..."
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In this paper we refer to the Temporal Precedence Problem on Pure Pointer Machines. This problem asks for the design of a data structure, maintaining a set of stored elements and supporting the following two operations: insert and precedes. The operation insert(a) introduces a new element a in the structure, while the operation precedes(a, b) returns true i# element a was inserted before element b temporally. In Ranjan et al. a solution was provided to the problem with worstcase time complexity O(log log n) per operation and O(n log log n) space, where n is the number of elements inserted. It was also demonstrated that the precedes operation has a lower bound of# (log log n) for the Pure Pointer Machine model of computation. In this paper we present two simple solutions with linear space and worstcase constant insertion time. In addition, we describe two algorithms that can handle the precedes(a, b) operation in O(log log d) time, where d is the temporal distance between the elements a and b.
Simple Confluently Persistent Catenable Lists.
, 1999
"... Abstract We consider the problem of maintaining persistent lists subject to concatenation and to insertions and deletions at both ends. Updates to a persistent data structure are nondestructive each operation produces a new list incorporating the change, while keeping intact the list or lists to wh ..."
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Abstract We consider the problem of maintaining persistent lists subject to concatenation and to insertions and deletions at both ends. Updates to a persistent data structure are nondestructive each operation produces a new list incorporating the change, while keeping intact the list or lists to which it applies. Although general techniques exist for making data structures persistent, these techniques fail for structures that are subject to operations, such as catenation, that combine two or more versions. In this paper we develop a simple implementation of persistent doubleended queues with catenation that supports all deque operations in constant amortized time. Our implementation is functional if we allow memoization.