Showing papers by "Gerth Stølting Brodal published in 1998"

Worst-case efficient external-memory priority queues

Abstract: A priority queue Q is a data structure that maintains a collection of elements, each element having an associated priority drawn from a totally ordered universe, under the operations Insert, which inserts an element into Q, and DeleteMin, which deletes an element with the minimum priority from Q. In this paper a priority-queue implementation is given which is efficient with respect to the number of block transfers or I/Os performed between the internal and external memories of a computer. Let B and M denote the respective capacity of a block and the internal memory measured in elements. The developed data structure handles any intermixed sequence of Insert and DeleteMin operations such that in every disjoint interval of B consecutive priorityqueue operations at most clogM/B N/M I/Os are performed, for some positive constant c. These I/Os are divided evenly among the operations: if B ≥ clogM/B N/M, one I/O is necessary for every B/(clogM/B N/M)th operation and if B < clogM/B N/M, c/B log M/B N/M I/Os are performed per every operation. Moreover, every operation requires O(log2 N) comparisons in the worst case. The best earlier solutions can only handle a sequence of S operations with O(σ i=1 S 1/B log M/B Ni/M) I/Os, where N i denotes the number of elements stored in the data structure prior to the ith operation, without giving any guarantee for the performance of the individual operations.

Worst-Case Efficient External-Memory Priority Queues

Abstract: A priority queue Q is a data structure that maintains a collection of elements, each element having an associated priority drawn from a totally ordered universe, under the operations Insert, which inserts an element into Q, and DeleteMin, which deletes an element with the minimum priority from Q. In this paper a priority-queue implementation is given which is efficient with respect to the number of block transfers or I/Os performed between the internal and external memories of a computer. Let B and M denote the respective capacity of a block and the internal memory measured in elements. The developed data structure handles any intermixed sequence of Insert and DeleteMin operations such that in every disjoint interval of B consecutive priorityqueue operations at most clogM/B N/M I/Os are performed, for some positive constant c. These I/Os are divided evenly among the operations: if B ≥ clogM/B N/M, one I/O is necessary for every B/(clogM/B N/M)th operation and if B < clogM/B N/M, c/B log M/B N/M I/Os are performed per every operation. Moreover, every operation requires O(log2 N) comparisons in the worst case. The best earlier solutions can only handle a sequence of S operations with O(σ i=1 S 1/B log M/B Ni/M) I/Os, where N i denotes the number of elements stored in the data structure prior to the ith operation, without giving any guarantee for the performance of the individual operations.

Finger search trees with constant insertion time

Abstract: We consider the problem of implementing finger search trees on the pointer machine, i.e., how to maintain a sorted list such that searching for an element 2, starting the search at any arbitrary element f in the list, only requires logarithmic time in the distance between 2 and f in the list. We present the first pointer-based implementation of finger search trees allowing new elements to be inserted at any arbitrary position in the list in worst case constant time. Previously, the best known insertion time on the pointer machine was O(log* n), where n is the total length of the list. On a unit-cost RAM, a constant insertion time has been achieved by Dietz and Raman by using standard techniques of packing small problem sizes into a constant number of machine words. Deletion of a list element is supported in O(log* n) time, which matches the previous best bounds. Our data structure requires linear space.

Comparator Networks for Binary Heap Construction

Abstract: Comparator networks for constructing binary heaps of size n are presented which have size O(n log log n) and depth O(log n). A lower bound of n log log n — O(n) for the size of any heap construction network is also proven, implying that the networks presented are within a constant factor of optimal. We give a tight relation between the leading constants in the size of selection networks and in the size of heap construction networks.