Abstract
A simple variant of a priority queue, called a soft heap, is introduced. The data structure supports the usual operations: insert, delete, meld, and findmin. In order to beat the standard information theoretic bounds, the soft heap allows errors: occasionally, the keys of certain items are artificially raised. Given any 0 < ε < 1/2 and any mixed sequence of n operations, the soft heap ensures that at most εn keys are raised at any time. The amortized complexity of each operation is constant, except for insert, which takes O(log 1/ε) time. The soft heap is optimal. Also, being purely pointer-based, no arrays are used and no numeric assumptions are made on the keys. The novelty of the data structure is that items are moved together in groups, in a data-structuring equivalent of “car pooling.” The main application of the data structure is a faster deterministic algorithm for minimum spanning trees.
This work was supported in part by NSF Grant CCR-93-01254, NSF Grant CCR-96-23768, ARO Grant DAAH04-96-1-0181, and NEC Research Institute.
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References
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© 1998 Springer-Verlag Berlin Heidelberg
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Chazelle, B. (1998). Car-Pooling as a Data Structuring Device: The Soft Heap. In: Bilardi, G., Italiano, G.F., Pietracaprina, A., Pucci, G. (eds) Algorithms — ESA’ 98. ESA 1998. Lecture Notes in Computer Science, vol 1461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68530-8_3
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DOI: https://doi.org/10.1007/3-540-68530-8_3
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